Force

Daniel Bernoulli (Groningen, 8 February 1700 – Basel, 8 March 1782) was aDutch-Swiss mathematician and was one of the many prominent mathematicians in theBernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability andstatistics. Bernoulli’s work is still studied at length by many schools of science throughout the world. In Physics :- He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle’s law. 2] He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation. [9] Bernoulli’s principle is of critical use inaerodynamics. [4] Daniel Bernoulli, an eighteenth-century Swiss scientist, discovered that as the velocity of a fluid increases, its pressure decreases The relationship between the velocity and pressure exerted by a moving liquid is described by the Bernoulli’s principle: as the velocity of a fluid increases, the pressure exerted by that fluid decreases.

Airplanes get a part of their lift by taking advantage of Bernoulli’s principle. Race cars employ Bernoulli’s principle to keep their rear wheels on the ground while traveling at high speeds. The Continuity Equation relates the speed of a fluid moving through a pipe to the cross sectional area of the pipe. It says that as a radius of the pipe decreases the speed of fluid flow must increase and visa-versa. This interactive tool lets you explore this principle of fluids.

You can change the diameter of the red section of the pipe by dragging the top red edge up or down. Principle In fluid dynamics, Bernoulli’s principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid’s potential energy. [1][2] Bernoulli’s principle is named after the Dutch-Swiss mathematician Daniel Bernoulliwho published his principle in his book Hydrodynamica in 1738. 3] Bernoulli’s principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli’s equation. In fact, there are different forms of the Bernoulli equation for different types of flow. The simple form of Bernoulli’s principle is valid for incompressible flows (e. g. most liquid flows) and also for compressible flows (e. g. gases) moving at low Mach numbers. More advanced forms may in some cases be applied to compressible flows at higher Mach numbers(see the derivations of the Bernoulli equation).

Bernoulli’s principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a decrease in its static pressure andpotential energy.

If the fluid is flowing out of a reservoir the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit mass (the sum of pressure and gravitational potential ? g h) is the same everywhere. [4] Bernoulli’s principle can also be derived directly from Newton’s 2nd law. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline. [5][6] Fluid particles are subject only to pressure and their own weight.

If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest. ————————————————- Incompressible flow equation

In most flows of liquids, and of gases at low Mach number, the mass density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. For this reason the fluid in such flows can be considered to be incompressible and these flows can be described as incompressible flow. Bernoulli performed his experiments on liquids and his equation in its original form is valid only for incompressible flow. A common form of Bernoulli’s equation, valid at any arbitrary point along a streamline where gravity is constant, is: |  | |  |  | | | | | | | where: is the fluid flow speed at a point on a streamline, is the acceleration due to gravity, is the elevation of the point above a reference plane, with the positive z-direction pointing upward – so in the direction opposite to the gravitational acceleration,  is the pressure at the chosen point, and is the density of the fluid at all points in the fluid. For conservative force fields, Bernoulli’s equation can be generalized as:[7] where ? is the force potential at the point considered on the streamline. E. g. for the Earth’s gravity ?  gz. The following two assumptions must be met for this Bernoulli equation to apply:[7] * the fluid must be incompressible – even though pressure varies, the density must remain constant along a streamline; * friction by viscous forces has to be negligible. By multiplying with the fluid density ? , equation (A) can be rewritten as: or: where: is dynamic pressure, is the piezometric head or hydraulic head (the sum of the elevation z and the pressure head)[8][9] and  is the total pressure (the sum of the static pressure p and dynamic pressure q). 10] The constant in the Bernoulli equation can be normalised. A common approach is in terms of total head or energy head H: The above equations suggest there is a flow speed at which pressure is zero, and at even higher speeds the pressure is negative. Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoulli’s equation ceases to be valid before zero pressure is reached. In liquids – when the pressure becomes too low – cavitation occurs. The above equations use a linear relationship between flow speed squared and pressure.

At higher flow speeds in gases, or for sound waves in liquid, the changes in mass density become significant so that the assumption of constant density is invalid Simplified form In many applications of Bernoulli’s equation, the change in the ? g z term along the streamline is so small compared with the other terms it can be ignored. For example, in the case of aircraft in flight, the change in height z along a streamline is so small the ? g z term can be omitted. This allows the above equation to be presented in the following simplified form: where p0 is called total pressure, and q is dynamic pressure. 11] Many authors refer to the pressure p as static pressure to distinguish it from total pressure p0 and dynamic pressure q. In Aerodynamics, L. J. Clancy writes: “To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure. “[12] The simplified form of Bernoulli’s equation can be summarized in the following memorable word equation: static pressure + dynamic pressure = total pressure[12]

Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure p and dynamic pressure q. Their sum p + q is defined to be the total pressure p0. The significance of Bernoulli’s principle can now be summarized as total pressure is constant along a streamline. If the fluid flow is irrotational, the total pressure on every streamline is the same and Bernoulli’s principle can be summarized as total pressure is constant everywhere in the fluid flow. 13] It is reasonable to assume that irrotational flow exists in any situation where a large body of fluid is flowing past a solid body. Examples are aircraft in flight, and ships moving in open bodies of water. However, it is important to remember that Bernoulli’s principle does not apply in the boundary layer or in fluid flow through long pipes. If the fluid flow at some point along a stream line is brought to rest, this point is called a stagnation point, and at this point the total pressure is equal to the stagnation pressure.

Applicability of incompressible flow equation to flow of gases Bernoulli’s equation is sometimes valid for the flow of gases: provided that there is no transfer of kinetic or potential energy from the gas flow to the compression or expansion of the gas. If both the gas pressure and volume change simultaneously, then work will be done on or by the gas. In this case, Bernoulli’s equation – in its incompressible flow form – can not be assumed to be valid. However if the gas process is entirely isobaric, or isochoric, then no work is done on or by the gas, (so the simple energy balance is not upset).

According to the gas law, an isobaric or isochoric process is ordinarily the only way to ensure constant density in a gas. Also the gas density will be proportional to the ratio of pressure and absolute temperature, however this ratio will vary upon compression or expansion, no matter what non-zero quantity of heat is added or removed. The only exception is if the net heat transfer is zero, as in a complete thermodynamic cycle, or in an individualisentropic (frictionless adiabatic) process, and even then this reversible process must be reversed, to restore the gas to the original pressure and specific volume, and thus density.

Only then is the original, unmodified Bernoulli equation applicable. In this case the equation can be used if the flow speed of the gas is sufficiently below the speed of sound, such that the variation in density of the gas (due to this effect) along each streamline can be ignored. Adiabatic flow at less than Mach 0. 3 is generally considered to be slow enough. [edit]Unsteady potential flow The Bernoulli equation for unsteady potential flow is used in the theory of ocean surface waves and acoustics. For an irrotational flow, the flow velocity can be described as the gradient ?? f a velocity potential ?. In that case, and for a constant density? , the momentum equations of the Euler equations can be integrated to:[14] which is a Bernoulli equation valid also for unsteady – or time dependent – flows. Here ?? /? t denotes the partial derivative of the velocity potential ? with respect to time t, and v = |?? | is the flow speed. The function f(t) depends only on time and not on position in the fluid. As a result, the Bernoulli equation at some moment t does not only apply along a certain streamline, but in the whole fluid domain.

This is also true for the special case of a steady irrotational flow, in which case f is a constant. [14] Further f(t) can be made equal to zero by incorporating it into the velocity potential using the transformation Note that the relation of the potential to the flow velocity is unaffected by this transformation: ?? = ??. The Bernoulli equation for unsteady potential flow also appears to play a central role in Luke’s variational principle, a variational description of free-surface flows using the Lagrangian (not to be confused with Lagrangian coordinates). ————————————————- edit]Compressible flow equation Bernoulli developed his principle from his observations on liquids, and his equation is applicable only to incompressible fluids, and compressible fluids at very low speeds (perhaps up to 1/3 of the sound speed in the fluid). It is possible to use the fundamental principles of physics to develop similar equations applicable to compressible fluids. There are numerous equations, each tailored for a particular application, but all are analogous to Bernoulli’s equation and all rely on nothing more than the fundamental principles of physics such as Newton’s laws of motion or the first law of thermodynamics.

Compressible flow in fluid dynamics For a compressible fluid, with a barotropic equation of state, and under the action of conservative forces, [15]   (constant along a streamline) where: p is the pressure ? is the density v is the flow speed ? is the potential associated with the conservative force field, often the gravitational potential In engineering situations, elevations are generally small compared to the size of the Earth, and the time scales of fluid flow are small enough to consider the equation of state as adiabatic. In this case, the above equation becomes [16]   (constant along a streamline) here, in addition to the terms listed above: ? is the ratio of the specific heats of the fluid g is the acceleration due to gravity z is the elevation of the point above a reference plane In many applications of compressible flow, changes in elevation are negligible compared to the other terms, so the term gz can be omitted. A very useful form of the equation is then: where: p0 is the total pressure ?0 is the total density [edit]Compressible flow in thermodynamics Another useful form of the equation, suitable for use in thermodynamics, is: [17]

Here w is the enthalpy per unit mass, which is also often written as h (not to be confused with “head” or “height”). Note that  where ? is the thermodynamic energy per unit mass, also known as the specific internal energy. The constant on the right hand side is often called the Bernoulli constant and denoted b. For steady inviscid adiabatic flow with no additional sources or sinks of energy, b is constant along any given streamline. More generally, when b may vary along streamlines, it still proves a useful parameter, related to the “head” of the fluid (see below).

When the change in ? can be ignored, a very useful form of this equation is: where w0 is total enthalpy. For a calorically perfect gas such as an ideal gas, the enthalpy is directly proportional to the temperature, and this leads to the concept of the total (or stagnation) temperature. When shock waves are present, in a reference frame in which the shock is stationary and the flow is steady, many of the parameters in the Bernoulli equation suffer abrupt changes in passing through the shock. The Bernoulli parameter itself, however, remains unaffected.

An exception to this rule is radiative shocks, which violate the assumptions leading to the Bernoulli equation, namely the lack of additional sinks or sources of energy. ————————————————- Real-world application Condensation visible over the upper surface of a wing caused by the fall in temperature accompanying the fall in pressure, both due to acceleration of the air. In modern everyday life there are many observations that can be successfully explained by application of Bernoulli’s principle, even though no real fluid is entirely inviscid [21] and a small viscosity often has a large effect on the flow. Bernoulli’s principle can be used to calculate the lift force on an airfoil if the behaviour of the fluid flow in the vicinity of the foil is known. For example, if the air flowing past the top surface of an aircraft wing is moving faster than the air flowing past the bottom surface, then Bernoulli’s principle implies that the pressure on the surfaces of the wing will be lower above than below. This pressure difference results in an upwards lift force. nb 1][22] Whenever the distribution of speed past the top and bottom surfaces of a wing is known, the lift forces can be calculated (to a good approximation) using Bernoulli’s equations[23] – established by Bernoulli over a century before the first man-made wings were used for the purpose of flight. Bernoulli’s principle does not explain why the air flows faster past the top of the wing and slower past the underside. To understand why, it is helpful to understand circulation, the Kutta condition, and the Kutta–Joukowski theorem. The carburetor used in many reciprocating engines contains a venturi to create a region of low pressure to draw fuel into the carburetor and mix it thoroughly with the incoming air. The low pressure in the throat of a venturi can be explained by Bernoulli’s principle; in the narrow throat, the air is moving at its fastest speed and therefore it is at its lowest pressure. * The Pitot tube and static port on an aircraft are used to determine the airspeed of the aircraft. These two devices are connected to theairspeed indicator which determines the dynamic pressure of the airflow past the aircraft.

Dynamic pressure is the difference betweenstagnation pressure and static pressure. Bernoulli’s principle is used to calibrate the airspeed indicator so that it displays the indicated airspeed appropriate to the dynamic pressure. [24] * The flow speed of a fluid can be measured using a device such as a Venturi meter or an orifice plate, which can be placed into a pipeline to reduce the diameter of the flow. For a horizontal device, the continuity equation shows that for an incompressible fluid, the reduction in diameter will cause an increase in the fluid flow speed.

Subsequently Bernoulli’s principle then shows that there must be a decrease in the pressure in the reduced diameter region. This phenomenon is known as the Venturi effect. * The maximum possible drain rate for a tank with a hole or tap at the base can be calculated directly from Bernoulli’s equation, and is found to be proportional to the square root of the height of the fluid in the tank. This is Torricelli’s law, showing that Torricelli’s law is compatible with Bernoulli’s principle. Viscosity lowers this drain rate. This is reflected in the discharge coefficient, which is a function of the Reynolds number and the shape of the orifice. 25] * In open-channel hydraulics, a detailed analysis of the Bernoulli theorem and its extension were recently (2009) developed. [26] It was proved that the depth-averaged specific energy reaches a minimum in converging accelerating free-surface flow over weirs and flumes (also[27][28]). Further, in general, a channel control with minimum specific energy in curvilinear flow is not isolated from water waves, as customary state in open-channel hydraulics. * The Bernoulli grip relies on this principle to create a non-contact adhesive force between a surface and the gripper. [edit]

Throughout this trimester, we have completed several activities to help us answer our driving question of, “which Planets would be the most habitable and how can we determine this. ” In order to organize our process of learning and how we can find these planets, we divided the question Into three learning units. Our units Included Nuclear Reactions and Star, Waves and light, Analyzing stars, and Circular motion and orbits. Our first unit was Nuclear Reactions and Stars.

This unit was focused on teaching us the properties of nuclear reactions, where they occur, and how they help us find tars, relating directly to our driving unit. The main idea of this unit was that there are three types of nuclear reactions. Radioactive decay is the release of either an electron, a helium atom, or energy, In an unstable and large elements. Fission Is the process of when a neutron traveling at fast speeds strikes a large element, causing It to split into two elements and the release of usually around three neutrons. Finally, fusion occurs when two elements fuse together, producing a large amount of energy.

This process requires extreme heat, like that of stars, In order to create an environment where all molecules move around at fast speeds, making them susceptible to fusion. Therefore, stars produce extreme amounts of energy through fusion. The heat produced by the sun makes fusion happen all the time. Next, through learning the equation E=mica, we realized that even a small amount of mass loss, which occurs In fusion, produces a large amount of energy. To sum up this unit, we learned about the evolutionary paths of stars and how they are affected by their mass.

Basically, average mass stars go through a simple path of stellar nebula, prostate, average star, red giant, white dwarf. However, high mass stars go through a stellar nebula, high mass star, super red giant, supernova, then either a neutron star or black hole. It becomes a black hole only of its mass is incredibly high. In order to understand why this happens, we watched an understanding stars video and did some helpful bookwork. Stars go through this cycle as the balance between gravity and the stars outward force (usually fusion) changes.

As a star gets hot enough to start fusion and create a variety of new elements, it’s outward force increases, causing the star to expand. As star then begins to run out of fuel, the star begins to use larger elements, cooling the gas and causing it to spread outwards. Finally, as the star begins to lose all of Its elements to fuse, gravity breaks the gravitational equilibrium It once had and collapses the star. Through this unit, we learned how stars work and how nuclear reactions are what cause the release of energy in nature. Our second unit consisted of waves and light.

Now that we knew how stars work, we had to learn how we know so much about stars, how we find them, and how we find planets that orbit them. In order to accomplish this, we first investigated waves. I OFF eaves: transverse (electromagnetic) and longitudinal waves (sound). Then we learned that there are two speed equations for waves. One is the obvious s=d/t. The other equation, which is Just a derivative of this, is speed?wavelength * frequency. Through this, we could calculate the wavelength or frequency of any electromagnetic wave if we knew one or the other (because the speed is always a constant).

Next we learned about the electromagnetic spectrum. This is basically a list of electromagnetic waves from least energy (longest wavelength) to most energy (shortest wavelength). This allowed us to see how much we can not see and the frequencies of these waves. Furthermore, we learned the importance of intensity, in my opinion, the most important part of this unit. Intensity is defined as the amount of energy in a given area. Basically, as we move away from the source, the area the source occupies increases, thus decreasing the energy we feel or see.

Through the intensity lab, in which I did high tech, we figured that the relationship is an inverse square. Using our now known knowledge about intensity, waves, and luminosity(power output or dotage), we could now use the luminosity of the star to find the habitable zone. To do this, we used the equations given by the online activity, eventually allowing us to see if there was a habitable planet, usually fictional, in the stars zone. In unit three, we expanded on our star knowledge from unit one and two. One of the main projects we did in this unit was the star evaluation sheet.

We had to find a random star using the online planetarium given to us and then research it’s characteristics. Once we found a star we liked, we used websites, such as wisped, o find out the basics of the star. Through the website, we were able to find distance from the earth, Surface temperature, the star’s radius, the star’s mass, and its Luminosity. Using this information, we were able to use our past knowledge and equations and new equations (wavelength of peak emission=b/T where b is Wine’s displacement constant) in order to further our information about the star.

Next, we used the equation of r=((1360*Lasts/Lulus)/ in order to find the outer and inner edge of the stars habitable zone (using 720 and 1500 as established intensities for habitable zone edges). Then using what we knew about that mass, luminosity, and temperature of the star, we could use the H-R diagrams, which we learned about this unit doing book work, to determine the stage the star was in. Sadly, my star was a massive star in its supernatant stage.

Even though the star did have a useable habitable zone, the star’s life p was way too short, leading to the conclusion that my star shouldn’t be considered as a possibility for Project Cygnus colony ship. Furthermore, we also did an activity online in which we chose a star offered, figured out whether it had a planet orbiting it through the brightness dips in the graph), figured out the period of the planet (again through the amount of time it took for the brightness dips to occur), and then through a series of equations, we found the habitable zone and saw whether the planet was inside of the zone.

This unit helped expand our knowledge on stars and to fugue out how to find the habitable zones of stars and whether a planet is orbiting in that zone. Objects are able to travel in a circle and why two objects in orbit do not collide into each other. Through a series of readings and activities, such as the water demo, we earned that centripetal force is the force holding an object in circular motion and it points radically inward. However, this brought up a couple of questions. These included: “Why does the water in the cup during the water demo not fall out? ND Why do we not fall out of a reallocates when we are upside down. In order to answer both, we first looked at properties of an object traveling in a circular direction. First, we learned that centripetal equation is basically acceleration in a circular direction that points inward. In a object is traveling in a circular path, we can SE the equation centripetal acceleration=(tangential speed)AAA / the radius of the circle in meters. To find the tangential speed, the equation we used was speed?circumference of the circle/the period of the object.

This is basically speed?distance/time. These equations helped us do our buggy lab in which we found the centripetal acceleration and used this to help us find the amount of centripetal force (in Newton’s) by using the equation f=mass*acceleration. The mass was easily found via a scale and we used the equations given to help us find the acceleration. However, this still didn’t totally answer the question of why we do not all out of a roller coaster when we are upside down.

Through a presentation and a roller coaster Journal glasswork, we realized that the reason this happens is because there is a normal force caused by our speed and inertia that causes us to resist falling. Through all of this, I realized that this perfectly explained the driving question of this unit, which stated Why does the moon not crash into the planet it is orbiting, the earth? As a result of these activities, I understood that this is because the object is constantly accelerating towards the center, causing an elliptical like orbit where he planet never crashes.

In conclusion, this unit taught me why objects stay in orbit and the forces involved in circular motion. With still more to go in this unit, I am quite excited to see where this leads us. Overall, all of the activities we have done have lead us closer to answering our driving question of the unit, “What planets are habitable and how can we determine this. ” Through a series of activities, labs, and lectures, we have learned about the properties of stars and their orbiting planets, all of which have helped us determine information about stars and their orbiting planets.

This Is defined by Hooker’s Law shown below. F ? -xx The law of conservation of energy is that energy cannot be created or destroyed, it can only be changed from one form to another. This means that the total amount of energy in an isolated system is constant over time. This means that the only thing that can happen to energy in a closed system is that it can change from one form to another. In this experiment energy changes from elastic potential energy to kinetic energy to gravitational potential energy. Some energy is also lost due to friction which creates heat and sound during the experiment.

Initial = Final Eek + Pep gravitational I + Pep spring + E thermal I = Kef+ Pep gravitational f + Pep bring f + E thermal f + Neon- conservative This equation clearly shows the energy transfer during the experiment Including the energy lost In non-conservative forms such as heat and sound. Basic energy formulae were also used In this experiment In order to calculate energy as it changes form. Eek- move Pep gravitational MGM very important as it is used a wide variety of physical applications. It is especially relevant and applicable in situations which there is little to no friction, such as in astrophysics.

Energy and applied forces can be calculated in order to accurately determine values seen in the equations above. Method: The equipment was set up as indicated in figurer . The track was placed at such a gradient where the cart would not reach the top of the track or come to close to the censor after pushed by the compressed spring. It should also be noted that the gradient of the slope remained constant throughout both experiments. The readings were zeroed and data was then collected by the censors and graphed on the program Logger Pro.

Figure 1: Experimental setup For the first experiment, the cart was released from different heights on the ramp ND measurements of the force and compression of the spring were taken in order to be able to calculate the spring constant. For the second experiment the spring on the cart was compressed and the cart is placed then released using a hard object such as a ruler. The spring then pushed the cart up the track and the censors took the reading of the force, displacement, velocity and acceleration needed in order to calculate the energy as it changed form in the system.

Results: Measurements for finding the spring constant of the spring x = displacement of spring from equilibrium position. F = force applied by the spring on the cart. K = the spring constant of the spring. Table 1 : Measured displacement of the spring and force applied by the spring and the calculated spring constant results. The uncertainties for the displacement and the force were chosen because of the accuracy of the censors and the ruler respectively. The uncertainty of the spring constant was calculated by halving the range of the results.

Measurements for finding the total energy during the second experiment Value Symbol Result Initial Compression of Spring 0. 033 В± 0. 001 m SF 0. 018В±0. 001 m Velocity as cart leaves spring I 0. 75В±0. 05 runs-l Velocity Just before collision if 0. 69 В± 0. 05 runs-l Max distance traveled Adam 0. 661 В± 0. 005 m Position at random point DRP 0. 198В±0. 005 m Velocity at random point Table 2: Velocity and distance measurements taken by the censors in order to prove conservation of energy. The uncertainties for the each of the results were chosen because of the accuracy of the censors respectively.

Analysis: Finding the spring constant of the spring To find the spring constant we use Hooker’s Law (F = -xx). The negative sign shows that the spring is being compressed and can be ignored in this case. For the first value: x = 0. 010В±0. 001 m and 5. 7 В± 0. 3 = 570 ram-I This process was then repeated for each data value and then the average of the results was found to be 598 Nm-l. The uncertainty for the spring constant was calculated by halving the range of the values which was found to be В± 28. 5 Nm-l . This gives the final value for the spring constant of the spring to be 598 В± 28. 5 Nm-l .

Conservation of Energy Graph 1, 2,3: These graphs shows the carts velocity and position and well as the force exerted in the spring by the cart as it moves up and down the slanted track. Using he results found in Table 2, the elastic potential energy, gravitational potential energy and kinetic energy can be calculated at six points during the experiment. These points are; before the spring is released, Just after the cart loses contact, at the during the first collision, and at some point between the release and collision points above. Before the spring is released all the energy is stored as elastic potential energy in the spring.

This can be easily calculated using the spring constant and the displacement of the spring. K = experimentally measured spring constant = 598 Nm-l . = initial compression of the spring = 0. 33 m Just after the cart loses contact with the spring, we can assume that all of the elastic potential energy has been converted into purely kinetic energy. Kinetic energy can be calculated using the mass and velocity of the cart. M = mass of cart = 0. 521 keg v = velocity as cart leaves spring = 0. 75 ms-l At the top of the slope the cart has stopped as the energy has been converted into purely gravitational potential energy.

This can be calculated using the mass and height of the cart as well as gravity. G = acceleration due to gravity = 9. 81 ms-2 = maximum height = 0. 036 m The maximum height of the cart was found by first calculating the angle of the slop using trigonometry. = 3. 130 This angle was then used with the maximum distance traveled value to calculate the maximum height. Just before the spring hits the bottom again the energy is again kinetic. This can again be calculated using the mass and velocity of the cart. At a chosen point part way up the slope the total energy will be the kinetic energy at that point plus the potential energy at the point.

Quality International Textile Group is a diverse, innovative provider of global textile solutions and distinguished fabric brands to automotive, apparel, interior furnishing and industrial markets worldwide.

While excellence is the common thread that weaves throughout Quality International Textile, it is the uniquely combined threads of a global manufacturing platform, innovative products, state-of-the-art systems, and a dynamic team of forward-thinking professionals that create unparalleled opportunities and competitive advantages for our customer partners. Quality improvement involves identifying discrepancies within organizational processes that may not run as effectively as possible. Many organizations find that a process is adequate for a time, but could function more effectively with some tweaking.

An organization that strives for quality helps create an atmosphere based on teamwork and ensures that the entire organization will contribute to meeting the company’s ultimate goals. An effective evaluation process helps manage employees, offer suggestions, and a chance to set their career goals. The evaluation of an employee should have a positive influence on each individual employee regardless of the outcome. A major determinant of service quality centers on the people providing the service. Employee selection, training, motivation, supervision, and reward-all process relating to employees have a significant impact on quality. Burrill, 1999) Currently, there is no particular standardization for the process. Each manager evaluation process differs from another. Below is an “as is” flow chart of the current evaluation process that need to be analyzed. The description of the process is extremely limited because currently there is no strategic plan in place within the entire process. Form the period that the self- evaluation is initiated until the time the management evaluates the employee can range any where from 1 month until one year. There is also no set timeframe when management discuses the employee evaluation until the time a pay increase is initiated.

All raised vary from one manager to another, and there is no particular percentage set for pay increases regardless of the evaluation outcome. Therefore, there is no relation of the process to the organization’s strategic plan. This process of improvement would benefit the employee; it would also benefit customers, and the company as a whole. Effective quality management for an evaluation process would lead to higher productivity because employees would know and understand that their yearly salary increase would depend on their performance therefore, timely and systematic resolution of evaluations/ appraisals is important.

An effective performance appraisal process would help the quality culture within the organization because employees would feel that their performance is significant to the company and its goals. Customers within the organization that are affected are office and field employees, suppliers, and customer. Initially a customer does not know if the service provided is good or bad, but an inefficient process for serving the customer can create a dad impression. The Fabric industry experiences the same business malfunctions as other companies.

Therefore, the fabric industry should adapt the methods and ideas as other companies but many still have not adopted the Total Quality Management process. Those are the companies that will most likely experience increasing competition, rising legal cost related to cost overruns and schedule delays, and decreasing profit margins. (Cotinas, 1999). Several steps can be taken to ensure that metrics motivate process behaviors that increase customer value. The first is to identify and prioritize the customers served by the process. (Burrill, 1999).

Although the process of employee evaluations does not directly involve customer service, it does have an effect on customers receiving services from the company’s employees. To hire an HR manager to perform create and perform appraisals to better adhere to each employees qualifications would be a great way to implement a change. The cause-and-effect diagram is a method for analyzing a process. The diagram’s purpose is to relate causes and effects. The cause and effect diagram can become complex and make it difficult to identify the problem, but it would be well worth it.

If other all employees are allowed to help identify problems relating to the situation and provide a chronological view, that would be just what the company needed for restructuring of the company’s quality culture. Improvement process can vary and there are many tools to help organizations implement change. Seeking ideas and opinions from employees is one of the best techniques to identify whether or not any changes are necessary.

References

1. Achieving Quality through continual improvement . From University of Phoenix eBook library web site: https://ecampus. phoenix. edu/content/ebooklibrary/content/eReader. Cortinas, D 1999

Executive Summary The purpose of this report is to discuss the main theories, models, frameworks and issues in the area of operations management, using British Airways as a working model, throughout the report. It was prepares for a coursework assignment as part of a Operations Management Module Academic journals and books from the area of operations management were used to illustrate the main points in the report to give evidence and back up the information provided.

Key findings of this report show how quality impacts on the development of the operations strategy in British Airways and how the key elements of design contribute hugely in operations. The importance and role of supply chain was discussed and three quality control methods; Quality Sampling, Total Quality Management and ISO 9000 were evaluated to how they could improve the performance of British Airways. Conclusions were drawn and it was found that operations management, based on the points discussed is a major factor to an organisations success. Contents Page

Page Number 1. Introduction4 2. BA’s Main Transformation Process 5 & 6 3. Quality & Operations Strategy 7, 8 & 9 4. Design in Operations 10 4. 1Concept Generation10 2. Concept Screening10 4. 3Preliminary Design 10 & 11 4. 4Evaluation and Improvement11 4. 5Prototyping and final design 11 & 12 5. The Role of Supply Chain 13 1. Quality13 2. Speed14 3. Dependability14 4. Flexibility15 5. Cost15 6. Quality Control Methods16 1. Quality Sampling17 2. Total Quality Management 17 & 18 3. ISO 900018 7. Conclusions19 8.

References 20 & 21 1. Introduction This report has been issued by University as part of this Operations Management module, in which a company will be selected and used as a working model throughout the report. The chosen company that will be used in relation to operations management is British Airways (hereafter BA). The various elements of operations management will be researched and applied to BA’s main transformation process. This will be done using academic articles and books in the area of operations management to illustrate the main points.

The report will begin with an overview of BA’s main transformation process indicating key inputs and outputs and then investigate how quality might impact upon the development of the operation strategy. Next it will review the key elements of design and how this impacts on the operation. Finally the role of supply chain in BA’s operation will be discussed and three different quality control methods will be evaluated to show how these might improve the performance in operations. Conclusions will be drawn and any overriding management issues identified. . BA’s Main Transformation Process The transformation process is a “model that describes operations in terms of their input resources, transforming processes and outputs of goods or services” (Slack et al, 2008, Page 8) BA use their aircrafts and staff which allows passengers and freight to travel from one destination to another thus, making this BA’s main transformation process. The operations function of a business is the arrangement of the resources which are allocated to the production and delivery of an organisations goods and services.

Three roles that are important for an operations function are the implementer, supporter and driver of the business strategy. In this example the operations functions follows the inputs of the transformation process. BA’s main transformation process inputs are the 238 aircraft in service, 32 million passengers, and 760,000 tonnes of cargo that it carried in 2009/10 along with the pilots and cabin crew. These are the transforming resources which allow the operation to take place and results in the service being provided.

This uses the transformed resources which can be split into two types; facilities such as the buildings and equipment, and staff who are all the people involved in the operation in some way. (ba. com) “The main activities of British Airways Plc and its subsidiary undertakings are the operation of international and domestic scheduled air services for the carriage of passengers, freight and mail and the provision of ancillary services” As BA is one of the worlds largest airlines operating internationally, the transformation process can be complicated with many units or departments interconnecting and contributing to the overall operation.

Some of the operations with in BA include British Airways World Cargo carrying freight, mail and courier traffic. (ba. com) They key outputs of BA’s transformation process are the millions of transported passengers to over 300 worldwide destinations and the cargo including dangerous goods and live animals. The outputs are services and therefore intangible. 3. Quality & Operations Strategy Operations strategies plan how the function will achieve future goals which are aligned with the companies overall strategy.

This can be done by understanding current capabilities and limitations, exploiting current capabilities in quality and process innovation. The basic role of operations is to implement strategy. “Operations strategy concerns the pattern of strategic decisions and actions which set the role, objectives and activities of the operation” (Slack et al, 2007, Page 63) Operations are the resources that create products and services. There are four perspectives on operations strategy; top down, market requirements, bottom up and operations resources perspective.

BA states “Meeting the rising expectations of our customers’ remains central to our strategy of transforming British Airways into the world’s leading global premium airline” This includes investment in their staff, aeroplanes and facilities in order to provide a premium quality service to their customers. (ba. com) “Quality is consistent conformance to customers’ expectations” (Slack et al, 2007, Page 539) Relating this to the above strategy of BA the quality of the service would be the friendly and helpful cabin crew, the flight leaving on time, clean aircraft and baggage arriving at the same time and destination as the passenger. Punctuality ensures other operational processes run smoothly and remains a key factor in whether customers would recommend British airways to other travellers” (ba. com). Therefore if BA produces a quality service to all of its customers, it is likely that they will get more business through recommendations and giving them an advantage over other airlines. As the quality of service that BA provides is paramount to the customer and can be a deciding factor on repeat business, this will have to be incorporated to the overall operations strategy of the organisation for it to be a success.

In BA’s 2009/10 annual report and accounts their strategy and objectives include meeting customer needs and improving margins through new revenue streams. Total Quality Management can have an influential impact on this as quality can reduce costs and increase dependability. “Lowered total quality expenditures, increased level of quality and reallocation of quality resources to prevention and away from appraisal and defect/failure correction activities” (SAM Advanced Management Journal, 1990, Page 25). This supports the above strategy of BA. TQM enables the developing of strategic thinking due to its inter-disciplinary nature” (Journal of Manufacturing Technology Management, 2004, Page 264) Overall in respect to BA this means that there has to be quality control in place for the overall strategy to be successful. When developing the operations strategy, taking quality into consideration there may be a higher cost initially, however, referring to the research above costs may be reduced overall due to less errors and more emphasis being placed on prevention tactics. 4. Design in Operations

There are five stages of service design which will be looked at individually in relation to BA; 4. 1Concept Generation If BA were to introduce a new destination to the existing range that they already offer if they decide to follow the market requirement perspective which is “what the market position requires operations to do” (Slack et al, 2001, Page 65). A lot of people would have to be involved from management at the top down to the customers. Market research would be a good idea to get ideas and suggestions from the customers for the proposed new estination. “Operations strategy involves translating marketing requirements into operations decisions” (Slack et al, 2007, Page 63) 2. Concept Screening This stage involves the ides going through feasibility, acceptability and vulnerability evaluation. Questions such as are the resources such as aircrafts and staff available, will it be accepted and what may go wrong with it and will it all be answered and evaluated. At this stage the ideas will progressively get fewer as each one is evaluated until there is only one possibility left. . Preliminary Design Preliminary design is the identifying of component products and services in the package, which in this case is the new flight destination in BA and the process of this will also be defined at this stage. The components of the new flight destination may be the aircraft, cabin crew, pilot, information leaflets and arrangement of new flight path and times. BA is part of a mass service process type in which there are many customers transactions therefore there is limited contact time and not much room for customisation.

For example BA cannot put on a special journey for a single person as there are a range of pre-planned journeys for passengers to choose between. 4. Evaluation and Improvement Design evaluation and improvement is used to see if the preliminary design can be improves and this can be done using various techniques including quality function deployment, value engineering and taguchi methods. Looking at Quality Function Deployment (QFD), which is a technique used to ensure that the eventual design of BA’s service actually meets the needs of the customers.

For example the new flight destination would have to be where the customers want to go and figure how this can be achieved. 5. Prototyping and final design The final stage of design is to turn the design into a prototype. For the new flight destination this may be running the flight on a trial basis to get reactions and feedback from the BA customers. Through the design process the five performance objectives; quality, speed, dependability, flexibility and cost will be considered.

For example it can be decided if the quality of service will be the same as a regular flight or if it is going to be increased and marketed as a premium flight. Will the flight be dependable and be on a regular basis and will the cost be in relation to the service as mentioned above and if the customers will be willing to pay more. This would be classed as a product layout within BA which “involves locating the transforming resources entirely for the convenience of the transformed resources” (Slack et al, 2007, page 193).

The transforming resources being the people, for example in BA as they can move through the airport in a predetermined route to enable them to get to the aircraft. 5. 0The role of Supply Chain A supply chain can be described as “A linkage or strand of operations that provides goods and services through to end customers; within a supply network several supply chains will cross through an individual operation” (Slack et al, 2007, page 402) All supply chain management has a common objective to satisfy the end customer and in the case of BA this will be the people travelling on the flight or BA’s World Cargo.

As mentioned in the design process the five performance objectives; quality, speed, dependability, flexibility and cost will have to achieve appropriate levels in the supply chain. These can be looked at individually in relation to BA: 1. Quality For a flight many onboard services are required including the equipment food and drink. By the time the meal reaches the customer on the flight it has gone through many operations in the supply chain. It is important that at each stage there are minimal errors as this multiplies by the time it reaches the customer.

Each stage then needs to take responsibility for its own and their supplier’s performance. This can in turn, ensure that the supply chain can achieve a high level of customer satisfaction at the end and therefore increase the chance of returning custom. 2. Speed In relation to BA, speed can mean the time it takes a customer to be served from the time they request the item to when it arrives. For example, receiving a drink in-flight. A fast response may be achieved by ensuring there is enough resources and stock, such as flight attendants and beverages within the supply chain.

If there is a large amount of stock then the customers demand will be fulfilled. In order for this to be successful, the products received from further up the supply chain, such as from the manufacturers need to have fast throughput time. Achieving this allows the customer demands to be met if there is stock readily available. 3. Dependability This means that BA has to have to correct stock in the right place at the right time. The airline needs to have the correct number or supplies or more on board at the time of a flight take off to ensure the demands of the customers are met.

For example “If the individual operations in a chain do not deliver as promised on time, there will be a tendency for customers to over order, or order early, in order to provide some kind of insurance against late delivery” (Slack et al, 2007, page 404) A way that BA can control their “items of low value, fairly consistent usage and short lead time” (Tersine, 1982, page 432) such as beverages is the two bin re-ordering system. This is an effective way of controlling stock levels as it can easily be seen when the re-order point is reached. 4. Flexibility

Flexibility is the supply chains ability to manage changes and disturbances. If BA’s stock levels are managed this should allow flexibility so the end customer’s needs are met and done so in a responsive manner. For BA to be flexible all operations in the supply chain must also be flexible. 5. Cost At each operational stage of the supply chain costs are incurred in order to produce the final product or service. A way of reducing costs is through JIT. Just-in-time is a Japanese management philosophy which tries to eliminate waste and always improve productivity.

JIT has many roles to play in an organisation as “Continuous improvement processes are associated with JIT including product quality, process efficiency, information systems and operating value-added activities more effectively while eliminating non-value-added activities” (Wild, 2002, page 61) BA may also incur costs whilst finding the right suppliers or trying to find one supplier of there required costs to cut the cost of their transactions and come to a mutually beneficial agreement for both parties. 6. Quality Control Methods

Measures for quality characteristics within BA can include functionality which is how well the service does the job, for example taking people to their required destination safely. Appearance is another which relates to the decor and cleanliness of aircraft, lounges and crew. Reliability, consistency of the flight service and keeping to the allocated times is another characteristic which is important to the service that BA provides. Durability ensures that the service provided is up to date and relevant to the customers needs.

Recovery is the ease with which problems can be resolved and contact between airline staff and customers. These characteristics can be measured as variables and attributes. For quality control methods to take place operations must identify how the quality characteristics can be measured and a standard to which it can be checked against. As much of BA’s quality comes down to service it can be difficult to perceive as this has no quantified measure. Quality control uses statistics, process analysis and quality standards, these attempts are to solve the root cause of any quality problems.

Quality means “doing things right, first time, every time” (Slack et al, 2010, Page 505) and in turn this will have a positive effect on revenues costs and customer satisfaction. The techniques of controlling quality that will be looked at in relation to BA are; quality sampling, total quality management and ISO 9000. 1. Quality Sampling This can be done by handing out surveys towards the end of the flight to receive customer feedback. The results can then be used to determine whether or not the quality characteristics mentioned above are up to the correct standards as expected by the customers and what BA wants to achieve.

This will not be 100% checking as not every person will take the time to fill this out; however it can give a good indication of BA’s performance. The results of this can then be used to find areas that need to be approved for example the courtesy of the crew or areas that are positive such are the decor and cleanliness of the aircraft. Overall if action is taken this should help to improve the performance of BA. 2. Total Quality Management Total Quality Management, (TQM) means meeting the needs and expectations of customers.

This includes all costs associated with quality which are prevention, appraisal, internal and external failure costs. Prevention costs are used to save failures and errors occurring. This can be the training and development of personnel and designing and improving of services and aircrafts to reduce any quality problems. Appraisal costs that could be incurred with BA are the setting of sampling plans as mentioned above and also conducting customer surveys. Internal failure costs, dealt from within the BA may include lost time due to errors. For example if problems occur and a flight is delayed or unable to take off.

If a strategy is in place this could prevent this error from happening. Finally external failure costs which are errors going out of the operation to the customer. An example can be an annoyed customer who take up the time of staff at a check in desk. The main aim of TQM is that the processes and products will be continually improved. 3. ISO 9000 Without any quality control methods there is little or no basis to measure and monitor quality performance. Certification to the ISO 9000 standard demonstrates if an organisations quality of service and products are acceptable.

This may improve the performance of BA as it gives assurance to customers that the service has to be at a certain standard so therefore there could be an increase of custom. However this could prove costly to train staff and conducing audits. 7. Conclusions The main findings from this report were the effects of quality on the development of the operations strategy and how design also impacts on this within BA. It was shown how quality, speed, dependability, flexibility and cost form the basis to all the decisions that are made in the area of operations management.

It was found that meeting the rising expectations of BA’s customers was paramount and quality control remained central in this. It was suggested that BA could us a survey to receive feedback to work on and improve if appropriate. This could increase the standard of quality of service within the organisation. The five stages of design in operations; concept generation, concept screening, preliminary design, evaluation and improvement and prototyping and final design were identified and evaluated.

The role of supply chain was discussed against the five performance objectives; quality, speed, dependability, flexibility and cost will have to achieve appropriate levels in the supply chain. Quality and its importance were shown how it can improve the performance of BA. In final conclusion it as found that operations management, based on the points discussed is a major factor to an organisations success. 8. References LEONARD, D and MCADAM, R. , 2004. Total quality management in strategy and operations: dynamic grounded models, Journal of Manufacturing Technology Management. online]. 15(3). Pp. 254-266. Available from: http://www. emeraldinsight. com/journals. htm? issn=1741-038X&volume=15&issue=3&articleid=851034&show=html www. emeraldinsight. com [Accessed 12th December 2010] www. ba. com [Accessed throughout December 2010] SLACK, N. , CHAMBERS, S. and JOHNSTON, R. , 2007. Operations Management. 5th ed. Essex: Pearson Education Limited GILMORE, H. L. , 1990. Continuous Incremental Improvement: An Operations Strategy for Higher Quality, Lower Costs, and Global Competitiveness. SAM Advanced Management Journal. online]. 55(1). Pp. 21. Available from: http://web. ebscohost. com/ehost/detail? vid=10&hid=112&sid=a64d86a6-2b59-4820-89e8-685e3526e9e7%40sessionmgr110&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=buh&AN=4601151 [Accessed 13th December 2010] SLACK, N. , CHAMBERS, S. and JOHNSTONE, R. , 2001. Operations Management. 3rd ed. Essex: Pearson Education Limited WILD, T. , 2002. Best Practice in Inventory Management. 2nd ed. Oxford: Elsevier Science Ltd TERSINE, R J. , 1982. Principles of Inventory and Materials Management. nd ed. New York, NY: Elsevier Science Publishing Co. , Inc TANNINEN, K. , PUUMALAINEN, K. and SANDSTROM, J. M. , 2010. the power of TQM: analysis of its effects on profitability, productivity and customer satisfaction. Total Quality Management & Business Excellence. [online] 21(2) Pp. 171-184. Available from: http://web. ebscohost. com/ehost/detail? vid=7&hid=105&sid=15499fbe-0026-4e12-b2c1-b55559c94134%40sessionmgr114&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=buh&AN=47760259 [Accessed 16th December 2010]

This equipment is a benchtop unit designed to introduce students to pressure, pressure scales and common devices available to measure pressure. The equipment comprises a Dead-weight Pressure Calibrator to generate a number of predetermined pressures, connected to a Bourdon gauge and electronic pressure sensor to allow their characteristics, including accuracy and linearity, to be determined.

The Dead-weight Pressure Calibrator, Bourdon gauge and pressure sensor are mounted on a common PVC base plate. The electrical console is free standing. The Dead-weight Pressure Calibrator consists of precision ground piston and matching cylinder with a set of weights. In normal use the appropriate combination of weights is applied to the top of the piston, to generate the required predetermined pressure, and then the piston is set spinning, to reduce vertical friction, while the readings from the measuring devices are recorded.

The operating range of the Dead-weight Pressure Calibrator and instrumentation is 20 kNm-2 to 200 kNm-2. The Bourdon gauge and pressure sensor are mounted on a manifold block with a priming vessel to contain the hydraulic fluid which is chosen to be water for safety and ease of use. A priming valve between the reservoir and the manifold block allows the cylinder, manifold block and gauge on test to be easily primed with the water ready for use. A damping valve between the cylinder and the manifold block allow the flow f water to be restricted to demonstrate the application of damping. An additional isolating valve on the manifold block allows water to be drained from the manifold block or allows alternative devices to be connected for calibration. Such devices can be tested over the range 20 kNm-2 to 200 kNm-2. The Bourdon gauge supplied is a traditional industrial instrument with rotary scale and mechanical indicator. The gauge has a 6” diameter dial that incorporates an arbitrary scale calibrated in degrees of rotation (independent of unit pressure) in addition to the usual scale calibrated in units of kNm-2.

A clear acrylic front face allows observation of the Bourdon tube the mechanism that converts motion of the Bourdon tube to rotation of the indicator needle. The electronic pressure sensor supplied incorporates a semi-conductor diaphragm that deflects when pressure is applied by the working fluid. This deflection generates a voltage output that is proportional to the applied pressure. The pressure sensor should be connected to the socket marked ‘Pressure Sensor’ on the front of the console.

The power supply, signal conditioning circuitry etc are contained in a simple electrical console with appropriate current protection devices and an RCD for operator protection. The electrical console is designed to stand alongside the Dead-weight Pressure Calibrator on the bench top. All circuits inside the console are operated by a main on/off switch on the front of the console. 57 The various circuits inside the console are protected against excessive current by miniature circuit breakers, as follows: CONT O/P. This breaker protects the power supply and circuits inside the console.

This breaker protects the electrical output marked OUTPUT at the rear of the console. The socket is used to power the IFD3 interface used for data logging. The voltage from the pressure sensor is displayed on a digital meter on the electrical console. An additional conditioning circuit incorporates zero and p adjustments and allows the voltage output from the pressure sensor to be converted and displayed as a direct reading pressure meter calibrated in units of pressure. The zero control and p control are mounted on the front of the console for ease of use.

A selector switch allows the voltage from the sensor or the direct reading pressure reading to be displayed as required. The voltage from the pressure sensor is simultaneously connected to an I/O Port for the connection to a PC using an optional interface device (TH-IFD) with educational software package. Alternatively, the signal can be connected to a user supplied chart recorder if required. Before use, the priming vessel must be filled with clean water (preferably deionized or demineralised water) and the calibrator, Bourdon gauge and pressure sensor fully primed.

Operational procedures

This equipment has been designed to operate over a range of pressures from 0 kN/m2 to 200 kN/m2 may damage the pressure sensors. In order to avoid such damage, DO NOT APPLY CONTINUOUS PRESSURE TO THE TOP OF THE PISTON ROD WHEN THE PRIMING VALVE IS CLOSED except by the application of the masses supplied. An impulse may be applied to the piston when operating at a fluid pressure of less than 200 kN/m2. This procedure is described in Experiment P1.

The following procedure should be followed to prime the Dead-weight Calibrator and pressure sensors, prior to taking readings: Level the apparatus using the adjustable feet. A circular spirit level has been provided for this purpose, mounted on the base of the dead-weight calibrator. Check that the drain valve (at the back of the Bourdon gauge base) is closed. Fill the priming vessel with water (purified or de-ionized water is preferable). Open the damping valve and the priming valve. With no masses on the piston, slowly draw the piston upwards a distance of approximately 6 cm (i. a full stroke of the piston). This draws water from the priming vessel into the system. Firmly drive the piston downwards, to expel air from the cylinder back towards the priming vessel. Repeat these two steps until no more bubbles are visible in the system. It may be helpful to raise the central section of the return tube between the manifold block and the priming vessel. This will help to prevent air being drawn back into the system as the piston is raised. Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow ir to enter, and then close the priming valve. The following procedure describes the calibration of the semiconductor pressure sensor. The procedure differs if using the optional TH-303 software, in which case users should instead refer to the Help Text provided with the software. Remove the piston from the cylinder, and switch the selector knob on the console to ‘Pressure’. This the ‘zero’ control on the console until the display reads zero. This sets the first reference point for the sensor calibration. Return the piston to the cylinder, and reprime the system as described above.

Place all the supplied masses onto the piston, with the greatest mass (2 kg) being added last. This corresponds to an applied pressure of 200 kN/m2. Spin the piston, and adjust the ‘p’ control until the sensor output matches the applied pressure. This sets the second reference point for the calibration. The calibration may be tested by applying a mass to the piston, spinning the piston in the cylinder, and then comparing the applied pressure to the sensor output. Each kg of applied mass corresponds to 20 kN/m2 of applied pressure. This piston itself gives an applied pressure of 20 kN/m2.

Precision

How closely the results agree with each other. Actual difference Modulus of the difference between indicated value and actual value Accuracy Maximum difference between indicated pressure and actual pressure Percentage accuracy Greatest difference between of actual scale reading indicated pressure and actual pressure, as a percentage of the actual pressure. Percentage accuracy Greatest difference between of full-scale reading indicated pressure and actual pressure, as a percentage of the range. Mean Sum of results divided by number of results.

Absolute deviation Difference between a single result and the mean of several results Mean deviation Sum of the absolute deviations divided by the number of absolute deviations Standard deviation Commonly used value in analysis of statistical data. The measurement of any physical property relies upon comparison with some fixed reference point. Pressure is one such property, and pressure measurement must begin by defining a suitable fixed point. An obvious reference point is that of the ambient pressure of the surroundings.

Pressure scales have been based around a zero point of the pressure of the atmosphere at sea level. Pressures lower than atmospheric are assigned negative values; pressures higher than atmospheric have positive values. Gauges for measuring pressure give readings relative to this zero point, by comparing the pressure of interest to the pressure of the surrounding air. Pressure measured with such a gauge is given relative to a fixed value, and is sometimes termed gauge pressure. Gauge measure pressure difference between the pressure to be measured and the barometric (ambient) pressure.

This may then need adjusting, to take into account any difference between barometric pressure and the pressure at sea level. Many calculations using equations derived from fundamental physical laws require absolute pressure values. Absolute pressure is the pressure relative to a total absence of pressure (i. e. a total vacuum). On an absolute pressure scale, all pressures have a positive value.

The following information may be of use when using this apparatus:

1. Operating range of dead-weight pressure calibrator
2. Diameter of dead-weight calibrator piston
3. Cross-sectional calibrator area of dead-weight
4. Pressure produced in cylinder by mass of piston with no applied masses
5. Approximate capacity of priming vessel.

• To gain a basic understanding of the concept of pressure and its measurement.
• To investigate the behavior of two kinds of pressure sensor, and the effect of damping on pressure measurement.
• To gain a basic understanding of the concept of pressure and its measurement.
• To investigate the behaviour of two kinds of pressure sensor
• To observe the effect of damping on pressure measurement

Method

To investigate the response of two kinds of pressure sensor to a pressure applied by a dead-weight calibrator device. To investigate the response of these sensors to the application of a sudden pressure spike, with varying levels of restriction of the liquid between the pressure application and the sensor.

Theory

Pressure is the force exerted by a medium, such as a fluid, on an area. In the TH2 apparatus, pressure is exerted by a piston on a column of water. The pressure applied is then equal to the force exerted by the piston over the cross-sectional area of the fluid. The use of the piston and masses with the cylinder generates a measurable reference pressure, Pa: Pa = Fa A 65 where Fa = gMa, and Fa = force applied to the liquid, Ma = total mass (incl. piston), and A = area of piston. The area of the piston can be expressed in terms of its diameter, d, as A = d2 4

The units of each variable must agree for the equations to be valid. Using SI units, Pa will be in Newtons per square metre (N/m, also known as Pascals) if Fa is in Newtons, A is in square metres, and d is in metres. The use of specific units of pressure will be covered in exercise B. For this exercise the area of the cylinder is a constant. The pressure can therefore be considered directly proportional to the mass applied to the mass on the piston Pressure measurement is normally concerned with measuring the effects of a pressure differential between two points in a fluid.

The simplest form of pressure sensor is a manometer tube, in which a tube of fluid is exposed at one end to the first point in the fluid, and at the other to the second point. Any pressure differential causes a displacement of fluid within the tube, which is proportional to the difference. Manometers (not included with the TH2 apparatus) are cheap, simple, and can be designed to cover a wide range of pressures. However, they are best used for measuring static pressures below about 600 kN/m, as the required height of the fluid becomes unworkable at greater pressures.

Their dynamic response is poor, so they are best suited to measuring static or slowly changing pressures. Some fluids used are toxic (such as mercury), and may be susceptible to temperature change. The Bourdon-type pressure gauge consists of a curved tube of oval cross-section. One end is closed, and is left free to move. The other end is left open to allow fluid to enter, and is fixed. The outside of the tube remains at ambient pressure. When fluid pressure inside the tube exceeds the pressure outside the tube, the section of the tube tends to 66 ecome circular, causing the tube to straighten (internal pressure lower than the ambient pressure conversely causes increased flattening, and the curve of the tube increases). A simple mechanical linkage transmits the movement of the free end of the tube to a pointer moving around dial. This type of gauge is one of the two kinds included in the TH2 apparatus. The second type of pressure gauge included as part of the TH2 is an electromechanical device. In a basic semiconductor pressure sensor, silicon strain gauges are fixed to one side of a diaphragm.

The two sides of the diaphragm are exposed to the two different pressures. Any pressure differential causes the diaphragm to expand towards the lower-pressure side, producing a change in the strain gauge voltage reading. The electronic semiconductor pressure sensor included with the TH2 is a more refined device with improved reliability and sensitivity for pressure measurement. It includes temperature compensation to reduce the effects of temperature variation on the results. The strain gauges used are formed by laying down a protective film of glass onto stainless steel, followed by a thin film of silicon.

The silicon is doped to produce semiconductor properties, and a mask is photoprinted onto it. The unmasked silicon is then removed, leaving a pattern of silicon semiconductor strain gauges molecularly bonded onto the surface of the steel. The gauges are connected to an Ohmmeter through a Wheatstone bridge, to amplify the signal produced. 67 In this type of sensor, a diaphragm is still used, but instead of fixing the strain gauges to the surface, the deflection of the diaphragm moves a steel force rod. This transfers the force to one end of the steel strip that the semiconductor resistors are bonded to.

The resulting deflection of the strip causes compression in some strain gauges, and tension in others, changing their resistance and producing a measurable output. Both the TH2 pressure sensors are set up to indicate the pressure differential between atmospheric pressure, and fluid pressurized with the use of the dead-weight calibrator. The fluid passes through a damping valve, positioned between the calibrator and the sensors. By partially closing the valve, fluid flow can be restricted. This affects the speed at which pressure is transferred from the point of application to the sensors.

Equipment set up

Level the apparatus using the adjustable feet. A circular spirit level has been provided for this purpose, mounted on the base of the dead-weight calibrator. Check that the drain valve (at the back of the Bourdon gauge base) is closed. Fill the priming vessel with water (purified or de-ionized water is preferable). Fully open the damping valve and the priming valve With no masses on the piston, slowly draw the piston upwards a distance of approximately 6cm (i. e. a full stroke of the piston). This draws water from the priming vessel into the system.

Firmly drive the piston downwards, to expel air from the cylinder back towards the priming vessel. Repeat these two steps until no more bubbles are visible in the system. It may be helpful to raise the central section of the return tube between the manifold block and 68 the priming vessel. This will help to prevent air being drawn back into the system as the piston is raised. Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow air to enter, and then close the priming valve.

Procedure

This equipment has been designed to operate over a range of pressure from 0 kN/m2 to 200 kN/m2. Exceeding a pressure of 200 kN/m2 may damage the pressure sensors. In order to avoid such damage, DO NOT APPLY CONTINUOUS PRESSURE TO THE TOP OF THE PISTON ROD WHEN THE PRIMING VALVE IS CLOSED except by application of the mass supplied. An impulse may be applied to the piston when operating at a fluid pressure of less than 200 kN/m2, as is described later in this procedure. Behavior of pressure sensors Spin the piston in the cylinder, to minimize friction effects between the piston and the cylinder wall.

While the piston is spinning, record the angle through which the Bourdon gauge needle has moved, and the voltage output of the electronic sensor. Apply a kg mass to the piston. Spin the piston and take a second set of readings for the Bourdon gauge needle angle and the electronic sensor. Repeat the procedure in kg increments. When using several masses, it will be necessary to place the 2 kg mass on top of the other masses. Repeat the procedure while removing the masses again, in kg increments. This gives two results for each applied mass, which may be averaged in order to reduce the effects of any error in an individual reading.

Effect of damping Apply a single mass to the piston, and spin it. While the piston is spinning, apply an impulse to the top of the piston by striking the top of the rod once, with the flat of the hand. Watch the behavior of the Bourdon gauge needle. Note the final sensor reading after the response settles. Slightly close the damping valve. Change the mass, spin the piston again, and apply an impulse to the rod. Observe any changes in the sensor responses. Repeat the procedure, closing the damping valve a little at a time and noting the response and the final sensor reading each time.

Results

Tabulate your results under the following headings:- 69 Mass applied to calibrator Mm (kg) Deflection of Bourdon gauge needle (degrees) Output from electrochemical pressure sensor (mV) Notes on sensor behavior (damping) Plot a graph of sensor response against applied mass for each sensor.

Ma is the total mass (including that of the piston) 71 g is the acceleration due to gravity, and A is the area of piston. The area of the piston can be expressed in terms of its diameter, d, as: A = d2 4 The pressure in the fluid may then be calculated in the relevant engineering units. These known pressures may then be compared to the pressure sensor outputs over a range of pressures. The relationship between sensor output and pressure may be turned into a direct scale, as on the Bourdon gauge scale. Alternatively, a reference graph may be produced.

Where the relationship is linear and the sensor output is electrical, the sensor may be calibrated using simple amplifier (a conditioning circuit). When using SI units, the units of pressure are Newtons per square meter (N/m, also known as Pascals). To calculate the pressure in N/m, M must be in kg, d in m, and g in m / s. For the pressure range covered in this exercise, it will be more convenient to use units of kN/m, where 1 kN/m = 1000 N/m (1 N/m = 0. 001 kN/m). Barometric pressure: pressure units and scale conversion Barometric pressures is usually measured in bar.

One bar is equal to a force of 105 N applied over an area of 1m. While bar and N/m have the same scale interval, pressure in bar often has a more convenient value when measuring barometric pressure. Pressure may also be measured in millimetres of mercury (mmHg). The pressure is given in terms of the height of a column of mercury that would be required to exert an equivalent pressure to that being measured. Another possible unit of measurement is atmospheres (atm). One standard atmosphere was originally defined as being equal to the pressure at sea level at a temperature of 15°C.

A pressure unit still in everyday use is pounds per square inch (psi or lbf / in.). One psi is equal to a weight of one pound applied over an area of 1 in.? If a barometer is available to measure the ambient pressure in the room where the equipment is located, the barometer reading should be converted SI units. Pressures may be converted from one scale to another using a conversion factor.

Take care not to damage the piston, as it is part of a high precision instrument and any damage will affect the accuracy of the experimental results. Level the apparatus using the adjustable feet. A circular spirit level has been mounted on the base of the dead weight calibrator for this purpose. Check that the drain valve (at the back of the Bourdon gauge base) is closed. Fill the priming vessel with water (purified or de-ionized water is preferable). Open the damping valve and the priming valve. 73 With no masses on the piston, slowly draw the piston upwards a distance of approximately 6cm (i. e. full stroke of the piston). This draws water from the priming vessel into the system. Firmly drive the piston downwards, to expel air from the cylinder back towards the priming vessel. Repeat these two steps until no more bubbles are visible in the system. It may be helpful to raise the central section of the return tube between the manifold block and the priming vessel. This will help to prevent air being drawn back into the system as the piston is raised. Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow air to enter, and then close the priming valve. Set the selector switch on the console to ‘Output’.

Procedure

This equipment has been designed to operate over a range of pressure from 0 kN/m2 to 200 kN/m2. Exceeding a pressure of 200 kN/m2 may damage the pressure sensors. In order to avoid such damage, DO NOT APPLY CONTINUOUS PRESSURE TO THE TOP OF THE PISTON ROD WHEN THE PRIMING VALVE IS CLOSED except by application of the mass supplied. Conversion of an arbitrary scale into engineering units Spin the piston to reduce the effects of friction in the cylinder. With the needle still spinning, record the angle indicated by the Bourdon gauge needle.

Place a kg mass on the piston, and spin the piston. Record the value of the applied mass, and the angle indicated by the Bourdon gauge needle. Increase the applied mass in increment of kg. Spin the piston and record the needle angle each increment. Repeat the measurements while decreasing the applied mass in steps of kg. This gives two readings for each applied mass, which may be averaged to reduce the effect of any error in an individual reading. Calculate the applied pressure at each mass increment. Calculate the average needle angle at each pressure increment.

Repeat the experiment, this time recording the applied mass and the indicated pressure on the Bourdon gauge scale. Compare this to the average needle angle recorded previously. Calibration of a semiconductor pressure sensor

Note

This procedure differs if the TH2-303 software is being used. Please refer to the online product Help Text if using this software. Spin the piston. Record the voltage indicated on the semiconductor output display on the console. Place a  kg mass on the piston, and spin the piston. Record the applied mass, and the voltage indicated on the semiconductor output display on the console.

Increase the applied mass in steps of kg, spinning the piston and recording the semiconductor output each time. Repeat the measurement while decreasing the applied mass in steps of kg. Calculate the applied pressure at each mass increment. Calculate the average sensor output at each pressure increment. Slowly open the priming valve. Open the valve to its maximum, and check that the damping valve is also fully open. The fluid in the system will now be at approximately atmospheric pressure (it will be slightly higher than atmospheric due to the height of fluid in the reservoir, but this is negligible compared to the range of the sensors).

Switch the selector knob on the console to PRESSURE. Turn the ZERO control on the console until the display read zero, to set the first reference point for the sensor calibration. Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow air to enter, and then close the priming valve. Place a large mass on the piston, and calculate the corresponding applied pressure. Spin the piston and adjust the SPAN control until the sensor output matches the applied pressure, to set the second reference point for the calibration. Remove the masses from the piston.

Take a set of readings from the calibrated semiconductor sensor, by adding masses to the piston in ? kg increments. Repeat the reading while decreasing the applied mass. This gives two reading for each applied mass, which may be averaged in order to reduce the effect of any error in an individual reading.

Results

Tabulate your results under the following headings: Barometric pressure Mass of piston Mp Diameter of cylinder, d Cross-sectional area of cylinder, A Mass on piston Mm (kg) Applied mass Ma (kg) Applied force Fa (N).

Needle angle N/m2 kg m m2 Indicated Indicated SemiBourdon conductor semiconductor pressure pressure output Pb Ps Pa E(mV) (N/m2) (degrees) (N/m2) (N/m2) Plot graphs of average needle angle against applied pressure for the Bourdon gauge, and voltage output against applied pressure for the semiconductor sensor. Plot a graph of indicated pressure against actual pressure for the Bourdon gauge and the calibrated semiconductor pressure sensor. If there is facility for measuring barometric pressure, it is possible to calculate the absolute pressure corresponding to each applied pressure increment.

The ambient pressure of the surroundings, Patm should be measured, then converted into N/m2 (if required). An additional column should be added to the results table: Absolute Pressure, Pabs (N/m2). Absolute pressure may then be calculated as Pabs = Pa + Patm. To investigate the sources of error when measuring pressure.

Method

Errors in measuring a quantity, such as pressure, can come from a number of sources. Some can be eliminated by careful choice of equipment and experimental method. Other errors are unavoidable, but can be minimized.

In any experiment, it is good practice to note any possible sources of error in the results, and to give an indication of the magnitude of such errors. Errors fall into three general categories:

Avoidable errors

These are errors that must be eliminated, as any results including such errors will often be meaningless. Such errors include:

• Incorrect use of equipment
• Incorrect recording of results
• Errors in calculations
• Chaotic errors, i. e. random disturbances, such as extreme vibration or electrical noise that are sufficient to mask the experimental results.

Random errors

Random errors should be eliminated if possible, by changing the design of the experiment or waiting until conditions are more favorable. Even if they cannot be eliminated, many random errors may be minimized by making multiple sets of readings, and averaging the results. Random errors include:

• Variation of experimental conditions (e. g. changes in ambient temperature)
• Variation in instrumentation performance
• Variation due to material properties and design (e. g. effect of friction)
• Errors of judgement (e. g. nconstancy in estimating a sensor reading)

Systematic errors

Systematic errors produce a constant bias or skew in the results, and should be minimized where possible. They include:

• Built-in errors (e. g. zero error, incorrect scale graduation)
• Experimental errors (due to poor design of the experiment or the apparatus)
• Systematic human errors (e. g. reading from the wrong side of a liquid meniscus)
• Loading error (errors introduced as a result of the act of measurement- for example, the temperature of a probe altering the temperature of the body being measured)

Errors may also be described in a number of ways:

• Actual difference – the difference between the indicated value (the value indicated by the gauge or sensor) and the actual scale reading (the true value of the property being measured). The actual value must be known to calculate the actual difference.
• Accuracy – the maximum amount by which the results vary from the actual value. The actual value must be known. Percentage accuracy of the actual scale reading – the greatest difference between the actual value and the indicated value, expressed as a percentage of the actual value.

The actual value must be known. Percentage accuracy of the full-scale reading (total range of the measurement device) – the greatest difference between the actual value and the indicated value, expressed as a percentage of the maximum value of the range being used. The actual value must be known.

• Mean deviation (or probable error) – The absolute deviation of a single result is the difference between a single result, and the average (mean) of several results. The mean deviation is the sum of the absolute deviations divided by their number. The actual value is not required. The mean deviation is an indication of how closely the results agree with each other.
• Standard deviation (or mean square error) – the standard deviation is the square root of the mean of the squares of the deviations (‘better’ results are obtained by dividing the sum of the values by the one less than the number of values). This is a common measure of the preciseness of a sample of data- how closely the results agree with each other. The actual value is not required.

Additional equipment

Values for the piston diameter and weight are provided. These may be replaced by your own measurements if desired.

The following equipment will be required to do so:

• Vernier callipers or a ruler, to measure the piston diameter
• A weigh-balance or similar, to measure the piston weight

To prime the cylinder, the following procedure should be followed (where this is required in the experiment): Level the apparatus using the adjustable feet. A circular spirit level has been mounted on the base of the dead weight calibrator for this purpose. Check that the drain valve (at the back of the Bourdon gauge base) is closed. Fill the priming vessel with water (purified or de-ionized water is preferable).

Fully open the damping valve and the priming valve. With no masses on the piston, slowly draw the piston upwards a distance of approximately 6cm (i. e. a full stroke of the piston). This draws water from the priming vessel into the system. Firmly drive the piston downwards, to expel air from the cylinder back towards the priming vessel. Repeat these two steps until no more bubbles are visible in the system. It may be helpful to raise the central section of the return tube between the manifold block and the priming vessel. This will help to prevent air being drawn back into the system as the piston is raised.

Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow air to enter, then close the priming valve.

Procedure

This equipment has been designed to operate over a range of pressure from 0 kN/m2 to 200 kN/m2. Exceeding a pressure of 200 kN/m2 may damage the pressure sensors. In order to avoid such damage, DO NOT APPLY CONTINUOUS PRESSURE TO THE TOP OF THE PISTON ROD WHEN THE PRIMING VALVE IS CLOSED except by application of the mass supplied. The following experiments give suggested ways in which particular sources of error may be investigated.

It is recommended that only one or two be attempted in a single laboratory session, with each being repeated several times, giving multiple samples for the error analysis.

Basic Error Analysis

The accuracy of the semiconductor calibration may be investigated by performing standard error calculations on the calibrated sensor output, using the results obtained in Experiment P2. If results are not available for analysis, the following procedure should be followed: Slowly open the priming valve. Open the valve to its maximum, and check that the damping valve is also fully open.

The fluid in the system will now be at approximately atmospheric pressure (it will be slightly higher than atmospheric due to the height of fluid in the reservoir, but this is negligible compared to the range of the sensors). Switch the selector knob on the console to PRESSURE. Turn the ZERO control on the console until the display read zero, to set the first reference point for the sensor calibration. Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow air to enter, then close the priming valve. Place a large mass on the piston, and calculate the corresponding applied pressure.

Spin the piston, and adjust the SPAN control until the sensor output matches the applied pressure, to set the second reference point for the calibration. Remove the masses from the piston. Take a set of readings from the calibrated semiconductor sensor, adding masses to the pan in kg increments, and again while decreasing the applied mass. This provides two set of readings for data analysis. The experiment should be repeated to provide further sets of data. Avoidable errors: Incorrect use of equipment Level the apparatus using the adjustable feet.

A circular spirit level has been mounted on the base of the dead-weight calibrator for this purpose Check that the drain valve (at the back of the Bourdon gauge base) is closed, and the damping valve is fully open. Remove the piston from the cylinder, then fill the priming vessel with water (purified or de-ionized water is preferable). Close the priming valve, then replace the piston in the cylinder. Take a set of readings without priming the system first. Random errors: Friction effects Prime the system as described in the equipment set up instructions.

Tilt the board at an angle of about 5 to 10 degrees. Titling the apparatus in this way will exaggerate any friction effects, as the force applied by the piston will no longer be acting straight downwards on the column of fluids, but will have components acting at right-angles to cylinder wall. Spin the piston. Take one reading while the piston is spinning, then observe the behavior of the needle. Continue to watch the needle as the piston stops spinning, then make a note of the new gauge reading. Apply masses to the piston in ? kg increments.

At each step, spin the piston, note the sensor output, and then take a second reading after the piston stops spinning.

Systematic error

Zero error

Calibrate the semiconductor pressure sensor, but do not include mass of piston in the applied mass when calculating the applied pressure. Take a set of readings from the calibrated semiconductor sensor over a range of applied masses, now including the piston mass in the applied mass calculation.

Human error

Take a set or readings from the Bourdon gauge pressure scale, but stand at an angle to the dial face when taking each reading. Keep the same viewing angle for each reading. This illustrates the effect of parallax on the readings taken.

Tabulate your results under the headings on the following page: For each result, calculate the absolute difference, ea between indicated value Pi and the applied pressure Pa. 81 Find the maximum absolute difference, the accuracy ea max and use this value and the corresponding indicated pressure to calculate the % accuracy of actual scale reading and the % accuracy of full-scale reading (use a range of 200 kN/m2). Correlate the data for several test runs, to give a set of indicated pressure readings corresponding to a single applied pressure.

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