Physics 207 Lecture 20. Chapter 15, Fluids


 Vivian Ramsey
 4 years ago
 Views:
Transcription
1 Chapter 15, Fluids This is an actual photo of an iceberg, taken by a rig manager for Global Marine Drilling in St. Johns, Newfoundland. The water was calm and the sun was almost directly overhead so that the diver Physics 207: Lecture 20, Pg 1 Physics 207, Lecture 20, Nov. 10 Goals: Chapter 15 Understand pressure in liquids and gases Use Archimedes principle to understand buoyancy Understand the equation of continuity Use an idealfluid model to study fluid flow. Investigate the elastic deformation of solids and liquids Assignment HW9, Due Wednesday, Nov. 19 th Wednesday: Read all of Chapter 16 Physics 207: Lecture 20, Pg 2 Page 1
2 Fluids (Ch. 15) At ordinary temperature, matter exists in one of three states Solid  has a shape and forms a surface Liquid  has no shape but forms a surface Gas  has no shape and forms no surface What do we mean by fluids? Fluids are substances that flow. substances that take the shape of the container Atoms and molecules are free to move. No long range correlation between positions. Physics 207: Lecture 20, Pg 3 Fluids An intrinsic parameter of a fluid Density ρ = m V units : kg/m 3 = 103 g/cm 3 ρ(water) = x 10 3 kg/m 3 = g/cm 3 ρ(ice) = x 10 3 kg/m 3 = g/cm 3 ρ(air) = 1.29 kg/m 3 = 1.29 x 103 g/cm 3 ρ(hg) = 13.6 x10 3 kg/m 3 = 13.6 g/cm 3 Physics 207: Lecture 20, Pg 4 Page 2
3 Fluids Another parameter: Pressure p = F A Any force exerted by a fluid is perpendicular to a surface of contact, and is proportional to the area of that surface. Force (a vector) in a fluid can be expressed in terms of pressure (a scalar) as: r F = panˆ n A Physics 207: Lecture 20, Pg 5 What is the SI unit of pressure? A. Pascal B. Atmosphere C. Bernoulli D. Young E. p.s.i. Units : 1 N/m 2 = 1 Pa (Pascal) 1 bar = 10 5 Pa 1 mbar = 10 2 Pa 1 torr = Pa 1 atm = x10 5 Pa = 1013 mbar = 760 Torr = 14.7 lb/ in 2 (=PSI) Physics 207: Lecture 20, Pg 6 Page 3
4 Pressure vs. Depth Incompressible Fluids (liquids) When the pressure is much less than the bulk modulus of the fluid, we treat the density as constant independent of pressure: incompressible fluid For an incompressible fluid, the density is the same everywhere, but the pressure is NOT! p(y) = p 0  y g ρ = p 0 + d g ρ Gauge pressure (subtract p 0, usually 1 atm) p 1 y 1 y 2 mg p 0 F 1 A F 2 p 2 F 2 = F 1 + m g = F 1 + ρvg F 2 /A = F 1 /A + ρvg/a p 2 = p 1  ρg y Physics 207: Lecture 20, Pg 7 Pressure vs. Depth For a uniform fluid in an open container pressure same at a given depth independent of the container y p(y) Fluid level is the same everywhere in a connected container, assuming no surface forces Physics 207: Lecture 20, Pg 8 Page 4
5 Pressure Measurements: Barometer Invented by Torricelli A long closed tube is filled with mercury and inverted in a dish of mercury The closed end is nearly a vacuum Measures atmospheric pressure as One 1 atm = m (of Hg) Physics 207: Lecture 20, Pg 9 Exercise Pressure What happens with two fluids?? Consider a U tube containing liquids of density ρ 1 and ρ 2 as shown: ρ 2 d I ρ 1 Compare the densities of the liquids: (A) ρ 1 < ρ 2 (B) ρ 1 = ρ 2 (C) ρ 1 > ρ 2 Physics 207: Lecture 20, Pg 10 Page 5
6 Exercise Pressure What happens with two fluids?? Consider a U tube containing liquids of density ρ 1 and ρ 2 as shown: ρ 2 d I At the red arrow the pressure must be the same on either side. ρ 1 x = ρ 2 (d 1 + y) Compare the densities of the liquids: ρ 1 y (A) ρ 1 < ρ 2 (B) ρ 1 = ρ 2 (C) ρ 1 > ρ 2 Physics 207: Lecture 20, Pg 11 Archimedes Principle Suppose we weigh an object in air (1) and in water (2). W 1 W 2? How do these weights compare? W 1 < W 2 W 1 = W 2 W 1 > W 2 Buoyant force is equal to the weight of the fluid displaced Physics 207: Lecture 20, Pg 12 Page 6
7 The Golden Crown In the first century BC the Roman architect Vitruvius related a story of how Archimedes uncovered a fraud in the manufacture of a golden crown commissioned by Hiero II, the king of Syracuse. The crown (corona in Vitruvius s Latin) would have been in the form of a wreath, such as one of the three pictured from grave sites in Macedonia and the Dardanelles. Hiero would have placed such a wreath on the statue of a god or goddess. Suspecting that the goldsmith might have replaced some of the gold given to him by an equal weight of silver, Hiero asked Archimedes to determine whether the wreath was pure gold. And because the wreath was a holy object dedicated to the gods, he could not disturb the wreath in any way. (In modern terms, he was to perform nondestructive testing). Archimedes solution to the problem, as described by Vitruvius, is neatly summarized in the following excerpt from an advertisement: The solution which occurred when he stepped into his bath and caused it to overflow was to put a weight of gold equal to the crown, and known to be pure, into a bowl which was filled with water to the brim. Then the gold would be removed and the king s crown put in, in its place. An alloy of lighter silver would increase the bulk of the crown and cause the bowl to overflow. From Physics 207: Lecture 20, Pg 13 Archimedes Principle Suppose we weigh an object in air (1) and in water (2). How do these weights compare? W 1 < W 2 W 1 = W 2 W 1 > W 2 Why? Since the pressure at the bottom of the object is greater than that at the top of the object, the water exerts a net upward force, the buoyant force, on the object. W 1 W 2? Physics 207: Lecture 20, Pg 14 Page 7
8 Sink or Float? The buoyant force is equal to the weight of the liquid that is displaced. If the buoyant force is larger than the weight of the object, it will float; otherwise it will sink. FB mg y We can calculate how much of a floating object will be submerged in the liquid: Object is in equilibrium F B = mg ρ liquid g V liquid = ρ object g V object V V liquid object = ρ ρ object liquid Physics 207: Lecture 20, Pg 15 Bar Trick What happens to the water level when the ice melts? piece of rock on top of ice A. It rises B. It stays the same C. It drops Physics 207: Lecture 20, Pg 16 Page 8
9 Exercise V 1 = V 2 = V 3 = V 4 = V 5 m 1 < m 2 < m 3 < m 4 < m 5 What is the final position of each block? Physics 207: Lecture 20, Pg 17 Exercise V 1 = V 2 = V 3 = V 4 = V 5 m 1 < m 2 < m 3 < m 4 < m 5 What is the final position of each block? Not this But this Physics 207: Lecture 20, Pg 18 Page 9
10 Exercise Buoyancy A small lead weight is fastened to a large styrofoam block and the combination floats on water with the water level with the top of the styrofoam block as shown. Pb styrofoam If you turn the styrofoam + Pb upsidedown, What happens? (A) It sinks (B) styrofoam Pb (C) styrofoam Pb (D) styrofoam Pb Active Figure Physics 207: Lecture 20, Pg 19 Exercise Buoyancy A small lead weight is fastened to a large styrofoam block and the combination floats on water with the water level with the top of the styrofoam block as shown. Pb styrofoam If you turn the styrofoam + Pb upsidedown, What happens (assuming density of Pb > water)? (A) It sinks (B) styrofoam Pb (C) styrofoam Pb (D) styrofoam Pb Physics 207: Lecture 20, Pg 20 Page 10
11 Exercise More Buoyancy Two identical cups are filled to the same level with water. One of the two cups has plastic balls floating in it. Cup I Which cup weighs more? Cup II (A) Cup I (B) Cup II (C) the same (D) can t tell Physics 207: Lecture 20, Pg 21 Exercise More Buoyancy Two identical cups are filled to the same level with water. One of the two cups has plastic balls floating in it. Cup I Which cup weighs more? Cup II (A) Cup I (B) Cup II (C) the same (D) can t tell Physics 207: Lecture 20, Pg 22 Page 11
12 Exercise Even More Buoyancy A plastic ball floats in a cup of water with half of its volume submerged. Next some oil (ρ oil < ρ ball < ρ water ) is slowly added to the container until it just covers the ball. Relative to the water level, the ball will: Hint 1: What is the buoyant force of the part in the oil as compared to the air? water oil (A) move up (B) move down (C) stay in same place Physics 207: Lecture 20, Pg 23 Exercise Even More Buoyancy A plastic ball floats in a cup of water with half of its volume submerged. Next some oil (ρ oil < ρ ball < ρ water ) is slowly added to the container until it just covers the ball. Relative to the water level, the ball will: Hint 1: What is the buoyant force of the part in the oil as compared to the air? water oil (A) move up (B) move down (C) stay in same place Physics 207: Lecture 20, Pg 24 Page 12
13 Pascal s Principle So far we have discovered (using Newton s Laws): Pressure depends on depth: p = ρ g y Pascal s Principle addresses how a change in pressure is transmitted through a fluid. Any change in the pressure applied to an enclosed fluid is transmitted to every portion of the fluid and to the walls of the containing vessel. Physics 207: Lecture 20, Pg 25 Pascal s Principle in action Consider the system shown: A downward force F 1 is applied to the piston of area A 1. F1 F 2 This force is transmitted through the liquid to create an upward force F 2. Pascal s Principle says that increased pressure from F 1 (F 1 /A 1 ) is transmitted throughout the liquid. d 1 A A 2 1 d 2 F 2 > F 1 with conservation of energy Physics 207: Lecture 20, Pg 26 Page 13
14 Exercise Hydraulics: A force amplifier Aka the lever Consider the systems shown on right. In each case, a block of mass M is placed on the piston of the large cylinder, resulting in a difference d i in the liquid levels. d A M If A 2 = 2 A 1, compare d A and d B A 1 A10 V 10 = V 1 = V 2 d A A 1 = d B A 2 d A A 1 = d B 2A 1 d B M d A = d B 2 A 2 A10 Physics 207: Lecture 20, Pg 27 Home Example Hydraulics: A force amplifier Aka the lever Consider the system shown on right. Blocks of mass M are placed on the piston of both cylinders. The small & large cylinders displace distances d 1 and d 2 Compare the forces on disks A 1 & A 2 ignoring the mass and weight of the fluid in this process M A 1 d 1 M A2 W 2 =  M g d 2 =  F 2 d 2 V 1 = V 2 = A 1 d 1 = A 2 d 2 W 1 = M g d 1 = F 1 d 1 W 1 + W 2 = 0 = F 1 d 1  F 2 d 2 F 2 d 2 = F 1 d 1 F 2 = F 1 d 1 / d 2 = F 1 A 2 / A 1 d 1 / d 2 = A 2 / A 1 implying P 1 = P 2 = F 1 /A 1 = F 2 /A 2 Physics 207: Lecture 20, Pg 28 Page 14
15 Fluids in Motion To describe fluid motion, we need something that describes flow: Velocity v There are different kinds of fluid flow of varying complexity nonsteady / steady compressible / incompressible rotational / irrotational viscous / ideal Physics 207: Lecture 20, Pg 29 Types of Fluid Flow Laminar flow Each particle of the fluid follows a smooth path The paths of the different particles never cross each other The path taken by the particles is called a streamline Turbulent flow An irregular flow characterized by small whirlpool like regions Turbulent flow occurs when the particles go above some critical speed Physics 207: Lecture 20, Pg 30 Page 15
16 Types of Fluid Flow Laminar flow Each particle of the fluid follows a smooth path The paths of the different particles never cross each other The path taken by the particles is called a streamline Turbulent flow An irregular flow characterized by small whirlpool like regions Turbulent flow occurs when the particles go above some critical speed Physics 207: Lecture 20, Pg 31 Onset of Turbulent Flow The SeaWifS satellite image of a von Karman vortex around Guadalupe Island, August 20, 1999 Physics 207: Lecture 20, Pg 32 Page 16
17 Ideal Fluids Fluid dynamics is very complicated in general (turbulence, vortices, etc.) Consider the simplest case first: the Ideal Fluid No viscosity  no flow resistance (no internal friction) Incompressible  density constant in space and time Simplest situation: consider ideal fluid moving with steady flow  velocity at each point in the flow is constant in time streamline A 2 A 1 In this case, fluid moves on streamlines v 1 v 2 Physics 207: Lecture 20, Pg 33 Ideal Fluids Streamlines do not meet or cross Velocity vector is tangent to streamline streamline A 2 A 1 Volume of fluid follows a tube of flow bounded by streamlines v 1 v 2 Streamline density is proportional to velocity Flow obeys continuity equation Volume flow rate Q = A v is constant along flow tube. A 1 v 1 = A 2 v 2 Follows from mass conservation if flow is incompressible. Physics 207: Lecture 20, Pg 34 Page 17
18 Exercise Continuity A housing contractor saves some money by reducing the size of a pipe from 1 diameter to 1/2 diameter at some point in your house. v 1 v 1/2 Assuming the water moving in the pipe is an ideal fluid, relative to its speed in the 1 diameter pipe, how fast is the water going in the 1/2 pipe? (A) 2 v 1 (B) 4 v 1 (C) 1/2 v 1 (D) 1/4 v 1 Physics 207: Lecture 20, Pg 35 Exercise Continuity v 1 v 1/2 (A) 2 v 1 (B) 4 v 1 (C) 1/2 v 1 (D) 1/4 v 1 For equal volumes in equal times then ½ the diameter implies ¼ the area so the water has to flow four times as fast. But if the water is moving four times as fast then it has 16 times as much kinetic energy. Something must be doing work on the water (the pressure drops at the neck and we recast the work as P V = (F/A) (A x) = F x ) Physics 207: Lecture 20, Pg 36 Page 18
19 Lecture 20, Nov. 10 Question to ponder: Does heavy water (D 2 0) ice sink or float? Assignment HW9, Due Wednesday, Nov. 19 th Wednesday: Read all of Chapter 16 Next slides are possible for Wednesday Physics 207: Lecture 20, Pg 37 Conservation of Energy for Ideal Fluid Recall the standard workenergy relation W = K = K f K i Apply the principle to a section of flowing fluid with volume V and mass m = ρ V (here W is work done on fluid) Net work by pressure difference over x ( x 1 = v 1 t) W = F 1 x 1 F 2 x 2 = (F 1 /A 1 ) (A 1 x 1 ) (F 2 /A 2 ) (A 2 x 2 ) = P 1 V 1 P 2 V 2 v 2 and V 1 = V 2 = V (incompressible) y 2 W = (P 1 P 2 ) V v 1 V p 2 y 1 p 1 Physics 207: Lecture 20, Pg 38 Page 19
20 W Conservation of Energy for Ideal Fluid = (P 1 P 2 ) V and W = ½ m v 2 2 ½ m v 1 2 = ½ (ρ V) v 2 2 ½ (ρ V) v 1 2 (P 1 P 2 ) = ½ ρ v 22 ½ ρ v 1 2 v 2 P 1 + ½ ρ v 1 2 = P 2 + ½ ρ v 2 2 = const. y 2 v 1 V p 2 y 1 p 1 Bernoulli Equation P 1 + ½ ρ v ρ g y 1 = constant Physics 207: Lecture 20, Pg 39 This leads to Conservation of Energy for Ideal Fluid P 1 + ½ ρ v 12 = P 2 + ½ ρ v 22 = const. and with height variations v 2 y 2 v 1 V p 2 y 1 p 1 Bernoulli s Equation P 1 + ½ ρ v ρ g y 1 = constant Physics 207: Lecture 20, Pg 40 Page 20
21 Bernoulli s Principle A housing contractor saves some money by reducing the size of a pipe from 1 diameter to 1/2 diameter at some point in your house. v 1 v 1/2 2) What is the pressure in the 1/2 pipe relative to the 1 pipe? (A) smaller (B) same (C) larger Physics 207: Lecture 20, Pg 41 Cavitation Venturi result In the vicinity of high velocity fluids, the pressure can gets so low that the fluid vaporizes. Physics 207: Lecture 20, Pg 42 Page 21
22 Applications of Fluid Dynamics Streamline flow around a moving airplane wing Lift is the upward force on the wing from the air Drag is the resistance The lift depends on the speed of the airplane, the area of the wing, its curvature, and the angle between the wing and the horizontal higher velocity lower pressure lower velocity higher pressure Note: density of flow lines reflects velocity, not density. We are assuming an incompressible fluid. Physics 207: Lecture 20, Pg 43 Elastic properties of solids : Some definitions Young s modulus: measures the resistance of a solid to a change in its length. L 0 L F elasticity in length Y = tensile tensile stress strain = F / A0 L / L 0 volume elasticity Bulk modulus: measures the resistance of solids or liquids to changes in their volume. F / A0 B = V / V 0 V 0 Physics 207: Lecture 20, Pg 44 F V 0  V Page 22
23 Physics 207: Lecture 20, Pg 45 EXAMPLE An irrigation system QUESTION: Physics 207: Lecture 20, Pg 46 Page 23
24 EXAMPLE An irrigation system Physics 207: Lecture 20, Pg 47 EXAMPLE An irrigation system Physics 207: Lecture 20, Pg 48 Page 24
25 EXAMPLE An irrigation system Physics 207: Lecture 20, Pg 49 EXAMPLE An irrigation system Physics 207: Lecture 20, Pg 50 Page 25
26 Elasticity Physics 207: Lecture 20, Pg 51 Elasticity F/A is proportional to L/L. We can write the proportionality as The proportionality constant Y is called Young s modulus. The quantity F/A is called the tensile stress. The quantity L/L, the fractional increase in length, is called strain. With these definitions, we can write Physics 207: Lecture 20, Pg 52 Page 26
27 EXAMPLE Stretching a wire QUESTIONS: Physics 207: Lecture 20, Pg 53 EXAMPLE Stretching a wire Physics 207: Lecture 20, Pg 54 Page 27
28 EXAMPLE Stretching a wire Physics 207: Lecture 20, Pg 55 Volume Stress and the Bulk Modulus Physics 207: Lecture 20, Pg 56 Page 28
29 Volume Stress and the Bulk Modulus A volume stress applied to an object compresses its volume slightly. The volume strain is defined as V/V, and is negative when the volume decreases. Volume stress is the same as the pressure. where B is called the bulk modulus. The negative sign in the equation ensures that the pressure is a positive number. Physics 207: Lecture 20, Pg 57 The figure shows volume flow rates (in cm 3 /s) for all but one tube. What is the volume flow rate through the unmarked tube? Is the flow direction in or out? A. 1 cm 3 /s, in B. 1 cm 3 /s, out C. 10 cm 3 /s, in D. 10 cm 3 /s, out E. It depends on the relative size of the tubes. Physics 207: Lecture 20, Pg 58 Page 29
30 Rank in order, from highest to lowest, the liquid heights h 1 to h 4 in tubes 1 to 4. The air flow is from left to right. A. h 1 > h 2 = h 3 = h 4 B. h 2 > h 4 > h 3 > h 1 C. h 2 = h 3 = h 4 > h 1 D. h 3 > h 4 > h 2 > h 1 E. h 1 > h 3 > h 4 > h 2 Physics 207: Lecture 20, Pg 59 Page 30
Physics 207 Lecture 18
Physics 07, Lecture 8, Nov. 6 MidTerm Mean 58.4 (64.6) Median 58 St. Dev. 6 (9) High 94 Low 9 Nominal curve: (conservative) 8000 A 679 B or A/B 346 C or B/C 933 marginal 98 D Physics 07: Lecture 8,
More informationPhysics 201 Lecture 26
Phsics 0 Lecture 6 Lecture 6 Goals: Understand pressure in s v Use rchimedes principle to understand buoanc v Understand the equation of continuit v Use an idealfluid model to stud fluid flow. luids l
More informationChapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian
Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite
More informationChapter 14. Fluid Mechanics
Chapter 14 Fluid Mechanics States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite volume nor shape All of these
More informationChapter 9: Solids and Fluids
Chapter 9: Solids and Fluids State of matters: Solid, Liquid, Gas and Plasma. Solids Has definite volume and shape Can be crystalline or amorphous Molecules are held in specific locations by electrical
More informationPhysics 207 Lecture 22. Lecture 22
Goals: Lecture Chapter 15 Use an idealfluid model to study fluid flow. Investigate the elastic deformation of solids and liquids Chapter 16 Recognize and use the state variables that characterize macroscopic
More informationNicholas J. Giordano. Chapter 10 Fluids
Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 10 Fluids Fluids A fluid may be either a liquid or a gas Some characteristics of a fluid Flows from one place to another Shape varies according
More informationPhysics 201 Chapter 13 Lecture 1
Physics 201 Chapter 13 Lecture 1 Fluid Statics Pascal s Principle Archimedes Principle (Buoyancy) Fluid Dynamics Continuity Equation Bernoulli Equation 11/30/2009 Physics 201, UWMadison 1 Fluids Density
More informationTOPICS. Density. Pressure. Variation of Pressure with Depth. Pressure Measurements. Buoyant ForcesArchimedes Principle
Lecture 6 Fluids TOPICS Density Pressure Variation of Pressure with Depth Pressure Measurements Buoyant ForcesArchimedes Principle Surface Tension ( External source ) Viscosity ( External source ) Equation
More informationChapter 9 Solids and Fluids. Elasticity Archimedes Principle Bernoulli s Equation
Chapter 9 Solids and Fluids Elasticity Archimedes Principle Bernoulli s Equation States of Matter Solid Liquid Gas Plasmas Solids: Stress and Strain Stress = Measure of force felt by material Stress= Force
More informationPhysics 201, Lecture 26
Physics 201, Lecture 26 Today s Topics n Fluid Mechanics (chapter 14) n Review: Pressure n Buoyancy, Archimedes s Principle (14.4) n Fluid Dynamics, Bernoulli s Equation (14.5,14.6) n Applications of Fluid
More informationFluid Mechanics. Chapter 12. PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman
Chapter 12 Fluid Mechanics PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 12 To study the concept of density
More informationChapter 12. Fluid Mechanics. A. The density ρ of a substance of uniform composition is defined as its mass M divided by its volume V.
Chapter 12 Fluid Mechanics 12.1 Density A. The density ρ of a substance of uniform composition is defined as its mass M divided by its volume V. That is,! = M V The density of water at 4 o C is 1000 kg/m
More informationStates of Matter. Chapter 9 Solids and Fluids. Solids: Stress and Strain. Solids: Stress and Strain. Stress = Force Area. Strain =!L L. Example 9.
Elasticity Chapter 9 Solids and Fluids Archimedes Principle Bernoulli s Equation Solid Liquid Gas Plasmas States of Matter Solids: Stress and Strain Solids: Stress and Strain Stress = Measure of force
More informationStates of Matter. Chapter 9 Solids and Fluids. Solids: Stress and Strain. Solids: Stress and Strain. Stress = Force Area. Strain =!
Elasticity Chapter 9 Solids and Fluids Archimedes Principle Bernoulli s Equation Solid Liquid Gas Plasmas States of Matter 1 2 Solids: Stress and Strain Solids: Stress and Strain Stress = Measure of force
More informationFluids, Continuity, and Bernouli
Fluids, Continuity, and Bernouli Announcements: Exam Tomorrow at 7:30pm in same rooms as before. Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/ Clicker question 1 A satellite, mass m,
More informationLecture 8 Equilibrium and Elasticity
Lecture 8 Equilibrium and Elasticity July 19 EQUILIBRIUM AND ELASTICITY CHAPTER 12 Give a sharp blow one end of a stick on the table. Find center of percussion. Baseball bat center of percussion Equilibrium
More informationPhysics 207 Lecture 21. Physics 207, Lecture 21, Nov. 12
Goals: Physics 207, Lecture 21, Nov. 12 Chapter 15 Use an idealfluid model to study fluid flow. Investigate the elastic deformation of solids and liquids Chapter 16 Recognize and use the state variables
More informationFluids. Fluid = Gas or Liquid. Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion
Chapter 14 Fluids Fluids Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion Fluid = Gas or Liquid MFMcGrawPHY45 Chap_14HaFluidsRevised 10/13/01 Densities MFMcGrawPHY45 Chap_14HaFluidsRevised
More informationPage 1. Physics 131: Lecture 23. Today s Agenda. Announcements. States of Matter
Physics 131: Lecture 3 Today s Agenda Description of Fluids at Rest Pressure vs Depth Pascal s Principle: hydraulic forces Archimedes Principle: objects in a fluid Bernoulli s equation Physics 01: Lecture
More informationChapter 9. Solids and Fluids. 1. Introduction. 2. Fluids at Rest. 3. Fluid Motion
Chapter 9 Solids and Fluids 1. Introduction 2. Fluids at Rest 3. Fluid Motion 1 States of Matter Solid Liquid Gas Plasma 2 Density and Specific Gravity What is Density? How do I calculate it? What are
More informationFluid Mechanics. If deformation is small, the stress in a body is proportional to the corresponding
Fluid Mechanics HOOKE'S LAW If deformation is small, the stress in a body is proportional to the corresponding strain. In the elasticity limit stress and strain Stress/strain = Const. = Modulus of elasticity.
More informationChapter 9. Solids and Fluids. States of Matter. Solid. Liquid. Gas
Chapter 9 States of Matter Solids and Fluids Solid Liquid Gas Plasma Solids Have definite volume Have definite shape Molecules are held in specific locations By electrical forces Vibrate about equilibrium
More information11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an
Chapter 11 Fluids 11.1 Mass Density Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an important factor that determines its behavior
More informationMECHANICAL PROPERTIES OF FLUIDS
CHAPTER10 MECHANICAL PROPERTIES OF FLUIDS QUESTIONS 1 marks questions 1. What are fluids? 2. How are fluids different from solids? 3. Define thrust of a liquid. 4. Define liquid pressure. 5. Is pressure
More informationMECHANICAL PROPERTIES OF FLUIDS:
Important Definitions: MECHANICAL PROPERTIES OF FLUIDS: Fluid: A substance that can flow is called Fluid Both liquids and gases are fluids Pressure: The normal force acting per unit area of a surface is
More informationFluids. Fluids in Motion or Fluid Dynamics
Fluids Fluids in Motion or Fluid Dynamics Resources: Serway  Chapter 9: 9.79.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT  8: Hydrostatics, Archimedes' Principle,
More informationFluid Mechanics. Chapter 14. Modified by P. Lam 6_7_2012
Chapter 14 Fluid Mechanics PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 6_7_2012 Goals for Chapter 14 To study
More informationChapter 9. Solids and Fluids
Chapter 9 Solids and Fluids States of Matter Solid Liquid Gas Plasma Solids Have definite volume Have definite shape Atoms or molecules are held in specific locations By electrical forces Vibrate about
More informationChapter 9. Solids and Fluids
Chapter 9 Solids and Fluids States of Matter Solid Liquid Gas Plasma Solids Have definite volume Have definite shape Molecules are held in specific locations By electrical forces Vibrate about equilibrium
More informationGeneral Physics I. Lecture 16: Fluid Mechanics. Prof. WAN, Xin ( 万歆 )
General Physics I Lecture 16: Fluid Mechanics Prof. WAN, Xin ( 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Motivations Newton s laws for fluid statics? Force pressure Mass density How to treat
More informationPhysics 201 Chapter 13 Lecture 1
Physics 201 Chapter 13 Lecture 1 Fluid Statics Pascal s Principle Archimedes Principle (Buoyancy) Fluid Dynamics Continuity Equation Bernoulli Equation 11/30/2009 Physics 201, UWMadison 1 Fluids Density
More informationFluid Mechanics. The atmosphere is a fluid!
Fluid Mechanics The atmosphere is a fluid! Some definitions A fluid is any substance which can flow Liquids, gases, and plasmas Fluid statics studies fluids in equilibrium Density, pressure, buoyancy Fluid
More informationPhysics 106 Lecture 13. Fluid Mechanics
Physics 106 Lecture 13 Fluid Mechanics SJ 7 th Ed.: Chap 14.1 to 14.5 What is a fluid? Pressure Pressure varies with depth Pascal s principle Methods for measuring pressure Buoyant forces Archimedes principle
More informationChapter 15: Fluids. Mass Density = Volume. note : Fluids: substances which flow
Fluids: substances which flow Chapter 5: Fluids Liquids: take the shape of their container but have a definite volume Gases: take the shape and volume of their container Density m ρ = V Mass Density =
More informationChapter 15: Fluid Mechanics Dynamics Using Pascal s Law = F 1 = F 2 2 = F 2 A 2
Lecture 24: Archimedes Principle and Bernoulli s Law 1 Chapter 15: Fluid Mechanics Dynamics Using Pascal s Law Example 15.1 The hydraulic lift A hydraulic lift consists of a small diameter piston of radius
More informationToday s Discussion: Fluids Pressure and Pascal s principle Bouyancy, Archimedes principle Bernoulli s equation
1 Physics 213 Waves, Fluids and Thermal Physics Summer 2007 Lecturer: Mike Kagan (mak411@psu.edu, 322 Whitmore) Today s Discussion: Fluids Pressure and Pascal s principle Bouyancy, Archimedes principle
More informationIf we change the quantity causing the deformation from force to force per unit area, we get a relation that does not depend on area.
2/24 Chapter 12 Solids Recall the rigid body model that we used when discussing rotation. A rigid body is composed of a particles constrained to maintain the same distances from and orientations relative
More informationChapter 9. Solids and Fluids 9.3 DENSITY AND PRESSURE
9.3 DENSITY AND PRESSURE Chapter 9 Solids and Fluids The density of an object having uniform composition is defined as its mass M divided by its volume V: M V [9.6] SI unit: kilogram per meter cubed (kg/m
More informationChapter 1 INTRODUCTION
Chapter 1 INTRODUCTION 11 The Fluid. 12 Dimensions. 13 Units. 14 Fluid Properties. 1 11 The Fluid: It is the substance that deforms continuously when subjected to a shear stress. Matter Solid Fluid
More informationGeneral Physics I (aka PHYS 2013)
General Physics I (aka PHYS 2013) PROF. VANCHURIN (AKA VITALY) University of Minnesota, Duluth (aka UMD) OUTLINE CHAPTER 12 CHAPTER 19 REVIEW CHAPTER 12: FLUID MECHANICS Section 12.1: Density Section 12.2:
More informationLiquids CHAPTER 13 FLUIDS FLUIDS. Gases. Density! Bulk modulus! Compressibility. To begin with... some important definitions...
CHAPTER 13 FLUIDS FLUIDS Liquids Gases Density! Bulk modulus! Compressibility Pressure in a fluid! Hydraulic lift! Hydrostatic paradox Measurement of pressure! Manometers and barometers Buoyancy and Archimedes
More informationCHAPTER 13. Liquids FLUIDS FLUIDS. Gases. Density! Bulk modulus! Compressibility. To begin with... some important definitions...
CHAPTER 13 FLUIDS Density! Bulk modulus! Compressibility Pressure in a fluid! Hydraulic lift! Hydrostatic paradox Measurement of pressure! Manometers and barometers Buoyancy and Archimedes Principle! Upthrust!
More informationUniversity Physics 226N/231N Old Dominion University. Ch 12: Finish Fluid Mechanics Exam Review
University Physics 226N/231N Old Dominion University Ch 12: Finish Fluid Mechanics Exam Review Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2016odu Wednesday, November
More informationChapter 14  Fluids. Archimedes, On Floating Bodies. David J. Starling Penn State Hazleton PHYS 213. Chapter 14  Fluids. Objectives (Ch 14)
Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced. Archimedes, On Floating Bodies David J.
More informationPhy 212: General Physics II. Daniel Bernoulli ( )
Phy 1: General Physics II Chapter 14: Fluids Lecture Notes Daniel Bernoulli (1700178) Swiss merchant, doctor & mathematician Worked on: Vibrating strings Ocean tides Kinetic theory Demonstrated that as
More informationChapter 10. Solids & Liquids
Chapter 10 Solids & Liquids Next 6 chapters use all the concepts developed in the first 9 chapters, recasting them into a form ready to apply to specific physical systems. 10.1 Phases of Matter, Mass Density
More informationFluid Dynamics. Equation of continuity Bernoulli s Equation Bernoulli s Application Viscosity Poiseuilles law Stokes law Reynolds Number
Fluid Dynamics Equation of continuity Bernoulli s Equation Bernoulli s Application Viscosity Poiseuilles law Stokes law Reynolds Number Fluids in Motion steady or laminar flow, if each particle of the
More informationcos(θ)sin(θ) Alternative Exercise Correct Correct θ = 0 skiladæmi 10 Part A Part B Part C Due: 11:59pm on Wednesday, November 11, 2015
skiladæmi 10 Due: 11:59pm on Wednesday, November 11, 015 You will receive no credit for items you complete after the assignment is due Grading Policy Alternative Exercise 1115 A bar with cross sectional
More informationCPO Science Foundations of Physics. Unit 8, Chapter 27
CPO Science Foundations of Physics Unit 8, Chapter 27 Unit 8: Matter and Energy Chapter 27 The Physical Properties of Matter 27.1 Properties of Solids 27.2 Properties of Liquids and Fluids 27.3 Properties
More informationPhysics 111. Thursday, November 11, 2004
ics Thursday, ember 11, 2004 Ch 15: Fluids Pascal s Principle Archimede s Principle Fluid Flows Continuity Equation Bernoulli s Equation Toricelli s Theorem Announcements Wednesday, 89 pm in NSC 118/119
More information2. For a S.H.O. determine, (a) the total energy (E), the kinetic and potential energies. of half amplitude:
The amplitude of vibration and hence, the energy transferred into the vibrating system is found to depend on the difference between f and, its maximum when the frequency of the external force is equal
More information9.4 A. Density The density of a substance of uniform composition is defined as its mass per unit volume (or mass:volume ratio)
Page 1 of 24 AP Physics Mechanics Chapter 910 Fluid Mechanics  Text Ch. 9  Select topics  9.49.7  Reading pp. 255263 textbook HW  #15,17,18,19,20,22,29,32,34,35,36,39,40 Ch 10  Select topics
More informationPHYSICS 220 Lecture 16 Fluids Textbook Sections
PHYSICS 220 Lecture 16 Fluids Textbook Sections 10.110.4 Lecture 16 Purdue University, Physics 220 1 States of Matter Fluids Solid Hold Volume Hold Shape Liquid Hold Volume Adapt Shape Gas Adapt Volume
More informationPhysics 123 Unit #1 Review
Physics 123 Unit #1 Review I. Definitions & Facts Density Specific gravity (= material / water) Pressure Atmosphere, bar, Pascal Barometer Streamline, laminar flow Turbulence Gauge pressure II. Mathematics
More informationStates of Matter Unit
Learning Target Notes Section 1: Matter and Energy What makes up matter? Matter is made of atoms and molecules that are in constant motion. Kinetic Theory of Matter A. Particles that make up matter are
More informationMULTIPLECHOICE PROBLEMS:(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)
MULTIPLECHOICE PROLEMS:(Two marks per answer) (Circle the Letter eside the Most Correct Answer in the Questions elow.) 1. The absolute viscosity µ of a fluid is primarily a function of: a. Density. b.
More informationPhysics 231 Lecture 23
Physics 31 Lecture 3 Main points of today s lecture: Gravitation potential energy GM1M PEgrav r 1 Tensile stress and strain Δ Y ΔL L 0 Bulk stress and strain: Δ V Δ P B Δ V Pressure in fluids: P ; Pbot
More information10  FLUID MECHANICS Page 1
0  FLUID MECHANICS Page Introduction Fluid is a matter in a state which can flow. Liquids, gases, molten metal and tar are examples of fluids. Fluid mechanics is studied in two parts: ( i ) Fluid statics
More informationSection 1 Matter and Energy
CHAPTER OUTLINE Section 1 Matter and Energy Key Idea questions > What makes up matter? > What is the difference between a solid, a liquid, and a gas? > What kind of energy do all particles of matter have?
More informationChapter 9 Fluids. Pressure
Chapter 9 Fluids States of Matter  Solid, liquid, gas. Fluids (liquids and gases) do not hold their shapes. In many cases we can think of liquids as being incompressible. Liquids do not change their volume
More informations and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I
Fundamentals of Engineering (FE) Exam General Section Steven Burian Civil & Environmental Engineering October 26, 2010 s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum
More informationPressure in a fluid P P P P
Fluids Gases (compressible) and liquids (incompressible) density of gases can change dramatically, while that of liquids much less so Gels, colloids, liquid crystals are all oddball states of matter We
More informationCh Buoyancy & Fluid Flow
Ch 12.35 Buoyancy & Fluid Flow PHYS 1210  Prof. JangCondell 1 Which grading system do you prefer for your final grade? A. Letter grades only (A, B, C, D, F) B. Plus/minus grading (A, A, B+, B, B,
More informationPhysics 220: Classical Mechanics
Lecture /33 Phys 0 Physics 0: Classical Mechanics Lecture: MWF 8:40 am 9:40 am (Phys 4) Michael Meier mdmeier@purdue.edu Office: Phys Room 38 Help Room: Phys Room schedule on course webpage Office Hours:
More informationm V DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: SI Unit of Mass Density: kg/m 3
Chapter 11 Fluids 11.1 Mass Density DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: ρ m V SI Unit of Mass Density: kg/m 3 11.1 Mass Density
More informationStates of matter. Density high > high >> low (pressure dependent)
Fluids States of matter Solids Fluids crystalline amorphous liquids gasses Interatomic forces strong > strong >> very weak Density high > high >> low (pressure dependent) Density is an important material
More informationPhysics 220: Classical Mechanics
Lecture 10 1/34 Phys 220 Physics 220: Classical Mechanics Lecture: MWF 8:40 am 9:40 am (Phys 114) Michael Meier mdmeier@purdue.edu Office: Phys Room 381 Help Room: Phys Room 11 schedule on course webpage
More informationMULTIPLECHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)
Test Midterm 1 F2013 MULTIPLECHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct nswer in the Questions Below.) 1. The absolute viscosity µ of a fluid is primarily a function
More informationSteven Burian Civil & Environmental Engineering September 25, 2013
Fundamentals of Engineering (FE) Exam Mechanics Steven Burian Civil & Environmental Engineering September 25, 2013 s and FE Morning ( Mechanics) A. Flow measurement 7% of FE Morning B. properties Session
More informationFluid: Air and water are fluids that exert forces on the human body.
Fluid: Air and water are fluids that exert forces on the human body. term fluid is often used interchangeably with the term liquid, from a mechanical perspective, Fluid: substance that flows when subjected
More informationPhysics 101: Lecture 17 Fluids
Exam III Physics 101: Lecture 17 Fluids Exam 2 is Mon Nov. 4, 7pm Extra office hours on Fri. (see webpage!) Physics 101: Lecture 17, Pg 1 Homework 9 Help A block of mass M 1 = 3 kg rests on a table with
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS OPTION B3: LUIDS Essential Idea: luids cannot be modelled as point particles. Their distinguishable response to compression from solids creates a set
More informationSummary PHY101 ( 2 ) T / Hanadi Al Harbi
الكمية Physical Quantity القانون Low التعريف Definition الوحدة SI Unit Linear Momentum P = mθ be equal to the mass of an object times its velocity. Kg. m/s vector quantity Stress F \ A the external force
More informationChapter 11. Fluids. continued
Chapter 11 Fluids continued 11.2 Pressure Pressure is the amount of force acting on an area: Example 2 The Force on a Swimmer P = F A SI unit: N/m 2 (1 Pa = 1 N/m 2 ) Suppose the pressure acting on the
More informationME 262 BASIC FLUID MECHANICS Assistant Professor Neslihan Semerci Lecture 4. (Buoyancy and Viscosity of water)
ME 262 BASIC FLUID MECHANICS Assistant Professor Neslihan Semerci Lecture 4 (Buoyancy and Viscosity of water) 16. BUOYANCY Whenever an object is floating in a fluid or when it is completely submerged in
More informationThere are three phases of matter: Solid, liquid and gas
FLUIDS: Gases and Liquids Chapter 4 of text There are three phases of matter: Solid, liquid and gas Solids: Have form, constituents ( atoms and molecules) are in fixed positions (though they can vibrate
More informationReminder: HW #10 due Thursday, Dec 2, 11:59 p.m. (last HW that contributes to the final grade)
Reminder: HW #0 due Thursday, Dec, :59 p.m. (last HW that contributes to the final grade) Recitation Quiz # tomorrow (last Recitation Quiz) Formula Sheet for Final Exam posted on Bb Last Time: Pressure
More informationChapter 10. Solids and Fluids
Chapter 10 Solids and Fluids Surface Tension Net force on molecule A is zero Pulled equally in all directions Net force on B is not zero No molecules above to act on it Pulled toward the center of the
More informationScience Is A Verb! Part 7. Let s do it! ISBN
Let s do it! Science Is A Verb! Part 7 ISBN 9781847003607 Contents INTRODUCTION Lab Title Where are we positioned? Students know position is defined in relation to some choice of a standard reference
More information5. is made of a different material than bar two
Example Problems: Bar one has a Young s modulus that is bigger than that of bar Two. This means that bar one: 1. is longer than bar two 2. is shorter than bar two 3. has a greater crosssectional area
More informationI N V E S T I C E D O R O Z V O J E V Z D Ě L Á V Á N Í
MECHNICS O LUIDS luids are both liquids and gases. The common property of fluids is that the particles can be separated easily (liquids do not have their own shape etc.). Real fluids have something like
More informationUnit 4: The Nature of Matter
16 16 Table of Contents Unit 4: The Nature of Matter Chapter 16: Solids, Liquids, and Gases 16.1: Kinetic Theory 16.2: Properties and Fluids 16.3: Behavior of Gases 16.1 Kinetic Theory Kinetic Theory kinetic
More informationChapter 18 Fluids Pearson Education, Inc. Slide 181
Chapter 18 Fluids Slide 181 Section 18.1: Forces in a fluid We dealt with solid objects in the previous chapters. We now turn our attention to liquids and gasses. Liquids and gasses are collectively called
More informationPressure in stationary and moving fluid Lab Lab On On Chip: Lecture 2
Pressure in stationary and moving fluid LabOnChip: Lecture Lecture plan what is pressure e and how it s distributed in static fluid water pressure in engineering problems buoyancy y and archimedes law;
More informationChapter 12: Gravity, Friction, & Pressure Physical Science, McDougalLittell, 2008
SECTION 1 (PP. 381388): GRAVITY IS A FORCE EXERTED BY MASSES. Georgia Standards: S8P3b Demonstrate the effect of balanced and unbalanced forces on an object in terms of gravity, inertia, and friction;
More informationPhysics 101: Lecture 18 Fluids II
Exam III Physics 101: Lecture 18 Fluids II Textbook Sections 9.6 9.8 Physics 101: Lecture 18, Pg 1 Review Static Fluids Pressure is force exerted by molecules bouncing off container P = F/A Gravity/weight
More informationStates of Matter. Physics 201, Lecture 25. Density ρ. Fluids
Physics 201, Lecture 25 Today s Topics n Fluid Mechanics (chapter 14) n Solids, Liquids, Gases, Plasmas n Pressure (14.1) n Pascal s Principle, Pressure Variation with Depth (14.2) n Pressure Measurement
More informationChapter 5(Section1) Friction in Solids and Liquids
Chapter 5(Section1) Friction in Solids and Liquids Que 1: Define friction. What are its causes? Ans : Friction: When two bodies are in contact with each other and if one body is made to move then the
More informationStevens High School AP Physics II Work for Notschool
1. (AP SAMPLE QUESTION) An ideal fluid is flowing with a speed of 12 cm/s through a pipe of diameter 5 cm. The pipe splits into three smaller pipes, each with a diameter of 2 cm. What is the speed of the
More informationSY 2018/ st Final Term Revision. Student s Name: Grade: 10A/B. Subject: Physics. Teachers Signature
SY 2018/2019 1 st Final Term Revision Student s Name: Grade: 10A/B Subject: Physics Teachers Signature Question 1 : Choose the correct answer : 1 ) What is the density of Mercury. a ) 13.6x10 3 b) 14.6x10
More informationPressure in stationary and moving fluid. LabOnChip: Lecture 2
Pressure in stationary and moving fluid LabOnChip: Lecture Fluid Statics No shearing stress.no relative movement between adjacent fluid particles, i.e. static or moving as a single block Pressure at
More informationPhysics 153 Introductory Physics II. Week One: FLUIDS. Dr. Joseph J. Trout
Physics 153 Introductory Physics II Week One: FLUIDS Dr. Joseph J. Trout joseph.trout@drexel.edu 6103486495 States (Phases) of Matter: Solid: Fixed shape. Fixed size. Even a large force will not readily
More informationPhysical Sciences 2: Assignments for Oct Oct 31 Homework #7: Elasticity and Fluid Statics Due Tuesday, Oct 31, at 9:30AM
Physical Sciences 2: Assignments for Oct. 24  Oct 31 Homework #7: Elasticity and Fluid Statics Due Tuesday, Oct 31, at 9:30AM After completing this homework, you should Be able to describe what is meant
More informationWelcome to: Physics I. I m Dr Alex Pettitt, and I ll be your guide!
Welcome to: Physics I I m Dr Alex Pettitt, and I ll be your guide! Interference superposition principal: most waves can be added y(x, t) =y 1 (x vt)+y 2 (x + vt) wave 1 + wave 2 = resulting wave y 1 +
More informationCHAPTER 6 Fluids Engineering. SKMM1922 Introduction of Mechanical Engineering
CHAPTER 6 Fluids Engineering SKMM1922 Introduction of Mechanical Engineering Chapter Objectives Recognize the application of fluids engineering to such diverse fields as microfluidics, aerodynamics, sports
More informationChapter 10  Mechanical Properties of Fluids. The blood pressure in humans is greater at the feet than at the brain
Question 10.1: Explain why The blood pressure in humans is greater at the feet than at the brain Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though
More informationFluid dynamics  Equation of. continuity and Bernoulli s principle.
Fluid statics Fluid dynamics  Equation of What is a fluid? Density Pressure Fluid pressure and depth Pascal s principle Buoyancy Archimedes principle continuity and Bernoulli s principle. Lecture 4 Dr
More informationb) (5) Find the tension T B in the cord connected to the wall.
General Physics I Quiz 6  Ch. 9  Static Equilibrium July 15, 2009 Name: Make your work clear to the grader. Show formulas used. Give correct units and significant figures. Partial credit is available
More informationChapter 15. m. The symbolic equation for mass density is: ρ= m V. Table of Densities
Chapter 15 Density Often you will hear that fiberglass is used for racecars because it is lighter than steel. This is only true if we build two identical bodies, one made with steel and one with fiberglass.
More information