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# Chapter13: Fluid Mechanics

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Chapter13: Fluid Mechanics, Kane

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### Chapter13: Fluid Mechanics

1. 1. Chapter 13 Fluid Mechanics ( )
2. 2. States of Matter  Solid   Liquid   Has a definite volume and shape Has a definite volume but not a definite shape Gas – unconfined  Has neither a definite volume nor shape
3. 3. States of Matter, cont   All of the previous definitions are somewhat artificial More generally, the time it takes a particular substance to change its shape in response to an external force determines whether the substance is treated as a solid, liquid or gas
4. 4. Fluids   A fluid is a collection of molecules that are randomly arranged and held together by weak cohesive forces and by forces exerted by the walls of a container Both liquids and gases are fluids
5. 5. Statics and Dynamics with Fluids  Fluid Statics   Fluid Dynamics   Describes fluids at rest Describes fluids in motion The same physical principles that have applied to statics and dynamics up to this point will also apply to fluids
6. 6. Forces in Fluids    Fluids do not sustain shearing stresses or tensile stresses ( ) The only stress that can be exerted on an object submerged( ) in a static fluid is one that tends to compress( ) the object from all sides The force exerted by a static fluid on an object is always perpendicular to the surfaces of the object
7. 7. Pressure(  The pressure P of the fluid at the level to which the device has been submerged is the ratio of the force to the area P F A )
8. 8. Pressure, cont  Pressure is a scalar quantity    Because it is proportional to the magnitude of the force If the pressure varies over an area, evaluate dF on a surface of area dA as dF = P dA Unit of pressure is pascal (Pa) 2 1Pa 1 N/m
9. 9. Pressure vs. Force   Pressure is a scalar and force is a vector The direction of the force producing a pressure is perpendicular to the area of interest
10. 10. Measuring Pressure    The spring is calibrated by a known force The force due to the fluid presses on the top of the piston and compresses the spring The force the fluid exerts on the piston is then measured
11. 11. Density Notes
12. 12. Density Table
13. 13. Variation of Pressure with Depth    Fluids have pressure that varies with depth If a fluid is at rest in a container, all portions of the fluid must be in static equilibrium All points at the same depth must be at the same pressure  Otherwise, the fluid would not be in equilibrium
14. 14. Pressure and Depth   Examine the darker region, a sample of liquid within a cylinder  It has a cross-sectional area A  Extends from depth d to d + h below the surface Three external forces act on the region
15. 15. Pressure and Depth, cont  The liquid has a density of    Assume the density is the same throughout the fluid This means it is an incompressible liquid The three forces are:    Downward force on the top, P0A Upward on the bottom, PA Gravity acting downward, Mg The mass can be found from the density: M V Ah
16. 16. Atmospheric Pressure ( )   If the liquid is open to the atmosphere, and P0 is the pressure at the surface of the liquid, then P0 is atmospheric pressure P0 = 1.00 atm = 1.013 x 105 Pa at see level
17. 17. Pascal’s Law (   ) The pressure in a fluid depends on depth and on the value of P0 Pascal’s law state that an increase in pressure at the surface must be transmitted to every other point in the fluid
18. 18. Pascal’s Principle • A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
19. 19. Pascal’s Law applications
20. 20. Archimedes’ principle
21. 21. Bernoulli’s principle • If the speed of a fluid element increases as the element travels along a horizontal streamline, the pressure of the fluid must decrease, and conversely.
22. 22. Temperature (     ) We associate the concept of temperature with how hot or cold an object feels Our senses provide us with a qualitative indication of temperature Our senses are unreliable for this purpose We need a reliable and reproducible method for measuring the relative hotness or coldness of objects  We need a technical definition of temperature
23. 23. Thermal Contact (  ) Two objects are in thermal contact with each other if energy can be exchanged between them   The exchanges we will focus on will be in the form of heat or electromagnetic radiation The energy is exchanged due to a temperature difference
24. 24. Thermal Equilibrium(  ) Thermal equilibrium is a situation in which two objects would not exchange energy by heat or electromagnetic radiation if they were placed in thermal contact  The thermal contact does not have to also be physical contact
25. 25. Zeroth Law of Thermodynamics  If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other   Let object C be the thermometer Since they are in thermal equilibrium with each other, there is no energy exchanged among them
26. 26. Zeroth Law of Thermodynamics, Example  Object C (thermometer) is placed in contact with A until they achieve thermal equilibrium   Object C is then placed in contact with object B until they achieve thermal equilibrium   The reading on C is recorded The reading on C is recorded again If the two readings are the same, A and B are also in thermal equilibrium
27. 27. Temperature – Definition   Temperature can be thought of as the property that determines whether an object is in thermal equilibrium with other objects Two objects in thermal equilibrium with each other are at the same temperature  If two objects have different temperatures, they are not in thermal equilibrium with each other
28. 28. Thermometers   A thermometer is a device that is used to measure the temperature of a system Thermometers are based on the principle that some physical property of a system changes as the system’s temperature changes
29. 29. Thermometers, cont  These properties include:        The volume of a liquid The dimensions of a solid The pressure of a gas at a constant volume The volume of a gas at a constant pressure The electric resistance of a conductor The color of an object A temperature scale can be established on the basis of any of these physical properties
30. 30. Thermometer, Liquid in Glass    A common type of thermometer is a liquid-inglass The material in the capillary tube ( ) expands as it is heated The liquid is usually mercury or alcohol
31. 31. Calibrating a Thermometer   A thermometer can be calibrated by placing it in contact with some natural systems that remain at constant temperature Common systems involve water    A mixture of ice and water at atmospheric pressure Called the ice point of water A mixture of water and steam in equilibrium Called the steam point of water Once these points are established, the length between them can be divided into a number of segments
32. 32. Celsius Scale  The ice point of water is defined to be 0o C  The steam point of water is defined to be 100o C  The length of the column between these two points is divided into 100 increments, called degrees
33. 33. Problems with Liquid-in-Glass Thermometers    An alcohol thermometer and a mercury thermometer may agree only at the calibration points The discrepancies between thermometers are especially large when the temperatures being measured are far from the calibration points The thermometers also have a limited range of values that can be measured   Mercury cannot be used under –39o C Alcohol cannot be used above 85o C
34. 34. Constant-Volume Gas Thermometer   The physical change exploited is the variation of pressure of a fixed volume gas as its temperature changes The volume of the gas is kept constant by raising or lowering the reservoir B to keep the mercury level at A constant
35. 35. Constant-Volume Gas Thermometer, cont    The pressure is indicated by the height difference between reservoir B and column A The thermometer is calibrated by using a ice water bath and a steam water bath The pressures of the mercury under each situation are recorded   The volume is kept constant by adjusting A The information is plotted
36. 36. Constant-Volume Gas Thermometer, final    To find the temperature of a substance, the gas flask is placed in thermal contact with the substance The pressure is found on the graph The temperature is read from the graph
37. 37. Absolute Zero    The thermometer readings are virtually independent of the gas used If the lines for various gases are extended, the pressure is always zero when the temperature is –273.15o C This temperature is called absolute zero
38. 38. Absolute Temperature Scale    Absolute zero is used as the basis of the absolute temperature scale The size of the degree on the absolute scale is the same as the size of the degree on the Celsius scale To convert:  TC = T – 273.15
39. 39. Absolute Temperature Scale, 2  The absolute temperature scale is now based on two new fixed points    Adopted by in 1954 by the International Committee on Weights and Measures One point is absolute zero The other point is the triple point of water This is the combination of temperature and pressure where ice, water, and steam can all coexist
40. 40. Absolute Temperature Scale, 3   The triple point of water occurs at 0.01o C and 4.58 mm of mercury This temperature was set to be 273.16 on the absolute temperature scale   This made the old absolute scale agree closely with the new one The units of the absolute scale are kelvins
41. 41. Absolute Temperature Scale, 4  The absolute scale is also called the Kelvin scale   The triple point temperature is 273.16 K   Named for William Thomson, Lord Kelvin No degree symbol is used with kelvins The kelvin is defined as 1/273.16 of the difference between absolute zero and the temperature of the triple point of water
42. 42. Some Examples of Absolute Temperatures    The figure at right gives some absolute temperatures at which various physical processes occur The scale is logarithmic The temperature of absolute zero cannot be achieved  Experiments have come close
43. 43. Fahrenheit Scale      A common scale in everyday use in the US Named for Daniel Fahrenheit Temperature of the ice point is 32oF Temperature of the steam point is 212oF There are 180 divisions (degrees) between the two reference points
44. 44. viscosity    The term viscosity is commonly used in the description of fluid flow to characterize the degree of internal friction in the fluid. This internal friction, or viscous force, is associated with the resistance that two adjacent layers of fluid have to moving relative to each other. Viscosity causes part of the kinetic energy of a fluid to be converted to internal energy. This mechanism is similar to the one by which an object sliding on a rough horizontal surface loses kinetic energy.