Note for PH 101 at UA-General Physics I (10)
Note for PH 101 at UA-General Physics I (10)
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Date Created: 02/06/15
GIANCOLI Lecture PowerPoints Chapter 10 Physics Principles with Applications 6 edition Giancoli Chapter 10 Units of Chapter 10 Phases of Matter Density and Specific Gravity Pressure in Fluids Atmospheric Pressure and Gauge Pressure Pascal s Principle Measurement of Pressure Gauges and the Barometer Buoyancy and Archimedes Principle Units of Chapter 10 Fluids in Motion Flow Rate and the Equation of Continuity Bernoulli s Equation Applications of Bernoulli s Principle from Torricelli to Airplanes Baseballs and TIA Viscosity Flow in Tubes Poiseuille s Equation Blood Flow Surface Tension and Capillarity Pumps and the Heart 101 Phases of Matter The three common phases of matter are solid liquid and gas A solid has a definite shape and size A liquid has a fixed volume but can be any shape A gas can be any shape and also can be easily compressed Liquids and gases both flow and are called fluids 102 Density and Specific Gravity The density p of an object is its mass per unit volume p 101 V The SI unit for density is kgm3 Density is also sometimes given in glcm3 to convert glcm3 to kgm3 multiply by 1000 Water at 4 C has a density of 1 gcm3 1000 kgm3 The specific gravity of a substance is the ratio of its density to that of water TABLE 10 1 Densities of Substancesf Densities of Substance Solids S O m 9 Aluminum 270 X 103 Iron andsteel 73 x 103 Copper 89 X 103 S b t Lead 113 x 103 u S a n Gold 193 x 103 Concrete 23 gtlt103 Granite 27 xii3 Wood typical 03A09 X 103 Glass common 2428 x 103 Ice H20 0917 x 103 Bone 1740 x 103 Liquid Water 4 C 100 gtlt103 Blood plasma 103 gtlt103 Bloodwhole 105 gtlt103 Sea water 1025 x 103 Mercury 136 X M3 Alcoholethyl 079 gtlt103 Gasoline 068 X103 Gases Air 129 Helium 0179 Carbon dioxide 198 Water steam 0598 100 C lDenSilies are given at 0 C and 1 alm pressure unless otherwise specified Copyright 2005 Pearson Prentice Hall Inc 103 Pressure in Fluids Pressure is defined as the force per unit area F 39 2 Pressure is a scalar the units of pressure in the SI system are pascals 1 Pa 1 Wm2 Q Pressure is the same in every v direction in a fluid at a given depth if it were not the fluid quot would flow 103 Pressure in Fluids Also for a fluid at rest there is no component of force parallel to any solid surface once again if there were the fluid would flow Copyright 2005 Pearson Prentice Hall Inc 103 Pressure in Fluids The pressure at a depth h below the surface of the liquid is due to the weight of the liquid above it We can quickly calculate 103 This relation is valid for any liquid whose density does not change with depth 104 Atmospheric Pressure and Gauge Pressure At sea level the atmospheric pressure is about 1013 X 105 Nm2 this is called one atmosphere atm Another unit of pressure is the bar 1bar 100 gtlt 105111112 Standard atmospheric pressure is just over 1 bar This pressure does not crush us as our cells maintain an internal pressure that balances it 104 Atmospheric Pressure and Gauge Pressure Most pressure gauges measure the pressure above the atmospheric pressure this is called the gauge pressure The absolute pressure is the sum of the atmospheric pressure and the gauge pressure Pamp 105 Pascal s Principle If an external pressure is applied to a confined fluid the pressure at every point within the fluid increases by that amount This principle is used for example in hydraulic lifts and hydraulic brakes b Master cylinder Pedal I ll AV Brake r Brake cylinder pads Disk attached to wheel Copyright 2005 Pearson Prentice Hall Inc Example Applying Pascal s Principle In the hydraulic lever below if the narrow piston has a circular crosssection of radius 5cm and the large piston has a circular crosssection of 10cm what is the input force needed a to raise an object of mass 1000kg 106 Measurement of Pressure Gauges and the Barometer There are a number of different types of pressure gauges This one is an open tube manometer The pressure in the open end is atmospheric pressure the pressure being measured will cause the fluid to rise until P the pressures on both gggfljggfeing sides at the same height are equal P P0 pgAh a Open tube manometer Example Pressure Gauge An opentube Po manometer filled with 1 water density 1000 kgm3 shows a height h g fang difference between its 39 quot two columns of 12 cm What is the measured ampemtubemammem pressure 106 Measurement of Pressure Gauges and the Barometer Scale Here are two more devices for d39 ma mg measurlng pressure the Atmospher K aneroid gauge and the tire pressure pressure gauge Dix Spring b Aneroid gauge used mainly for air pressure and then called an aneroid barometer Pressure of air in tire c Tire gauge 106 Measurement of Pressure Gauges and the Barometer P 0 A This is a mercury barometer developed by Torricelli to measure atmospheric pressure The height of the column of mercury is such that the pressure in the tube at the surface level is 1 atm 76 cm Therefore pressure is often quoted in millimeters or inches of mercury Copyright 2005 Pearson Prentice Hall Inc 106 Measurement of Pressure Gauges and the Barometer Any liquid can serve in a Torricellistyle barometer but the most dense ones are the most convenient This barometer uses water 107 Buoyancy and Archimedes Principle This is an object submerged in a fluid There is a net force on the object because the pressures at the top and bottom of it are different The buoyant force is F a found to be the upward x force on the same volume of water FB 2 F2 F1 2 ngAhquot2 11 ngAAh PFVE Archimedes Principle The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by that object When submerged an object displaces an amount of fluid equal to that object s volume We then calculate the weight of that volume of fluid and that gives us the buoyant force 107 Buoyancy and Archimedes Principle The net force on the object is then the difference between the buoyant force and the gravitational force illllilllli illllvllllli a 107 Buoyancy and Archimedes Principle If the object s density is less than that of water there will be an upward net force on it and it will rise until it is partially out of the water FB 2000 kgg FB 1200 kgg mg 1200 kgg a b Copyright 2005 Pearson Prentice Hall Inc 107 Buoyancy and Archimedes Principle For a floating object the fraction that is submerged is given by the ratio of the object s density to that of the fluid Vdisp V0 p f This is because the object will rise to the level where its weight equals the buoyant force F p V g B F ispl And the buoyant force I depends on the volume of fluid displaced which in turn is equal to the volume of the object which mg 2 pOVOg remains submerged Sinking vs Floating An object in a fluid will always displace a volume of fluid which is equal to the volume of the object underwater If the object is fully submerged this is the total volume of the object If the object is floating then the volume undenNater is less than the total volume Sinking vs Floating A submerged object will displace an amount of fluid equal to its volume If the object is denser than the fluid then the weight of fluid displaced which is the buoyancy force will be less than the weight of the weight of the object and the object will sink A floating object has its weight equal to the buoyant force The buoyant force depends on the volume of fluid displaced which depends on how much is below the fluid level The object then floats at a level where buoyant force equals weight 107 Buoyancy ancl Archimedes Principle FE This principle also works in the air this is why hotair and helium balloons rise Copyright 2005 Pearson Prentice Hall lnc Example Helium Balloon What volume of Helium is needed in a balloon to lift a load of 200 kg including the mass of the empty balloon gt FB 108 Fluids in Motion Flow Rate and the Equation of Continuity If the flow of a fluid is smooth it is called streamline or laminar flow a Above a certain speed the flow becomes turbulent b Turbulent flow has eddies the viscosity of the fluid is much greater when eddies are present Copyright 2005 Pearson Prentice Hall Inc 108 Fluids in Motion Flow Rate and the Equation of Continuity We will deal with laminar flow The mass flow rate is the mass that passes a given point per unit time The flow rates at any two points must be equal as long as no fluid is being added or taken away This gives us the equation of continuity P1141711 P2142 92 10394a 108 Fluids in Motion Flow Rate and the Equation of Continuity If the density doesn t change typical for liquids this simplifies to A1121 AM Where the pipe is wider the flow is slower Copyright 2005 Pearson Prentice Hall Inc Example Blood Flow Blood flows from the heart into the aorta and then through major arteries which eventually branch into many small capillaries The radius of the aorta is 12 cm and the speed of blood passing through it is about 40 cms Given that the average radius of a capillary is about 4 x 104 cm and blood flows through it with a speed of about 5 x 104 ms use the continuity equation for fluid flow to estimate the number of capillaries in the human body Arteries V valves c capillaries Copyright 2005 Pearson Prentice Hall Inc Veins 109 Bernoulli s Equation ANzk All AH gt 72 A fluid can also change its P2 height By looking at the A2 work done as it moves we 3 2 find a P p02 pgy constant All i 2 h This is Bernoulli s F equation One thing it tells us is that as the speed goes up the b pressure goes down Copyright 2005 Pearson Prentice Hall Inc Example Flow and Pressure in Hot Water System In a home hotwater system suppose water is pumped at a speed of 05 ms through a 40cm diameter pipe in the basement under a pressure of 30 atm What will be the flow speed and pressure in a 26 cm diameter pipe on the second floor 50 m above 1010 Applications of Bernoulli s Principle Using Bernoulli s principle we find that the speed of fluid coming from a spigot on an open tank is Uzzo I y2 Y1 a l C 01 U 1vm M 106 This is called Torricelli s theorem 1010 Applications of Bernoulli s Principle A jet of air has high Low veloc1ty and hence low P pressure As the ping pong ball tries to move out of the jet the surrounding air has higher pressure and that pushes the ball back into the jet High P no ow 1010 Applications of Bernoulli s Principle Lift on an airplane wing is due to the different air speeds and pressures on the two surfaces of the wing Lower pressure i Higher pressure 1010 Applications of Bernoulli s Principle TIA B s rv artery to brain A person with constricted arteries will find that they may experience a Left Right temporary lack of blood to Vert bral vertebral the brain TIA as blood artery asrtiryl speeds up to get past the Subclavian u C aV1an artery artery constriction thereby reducing the pressure Costriction Aorta Copyright 2005 Pearson Prentice Hall Inc Summary of Chapter 10 Phases of matter solid liquid gas Liquids and gases are called fluids Density is mass per unit volume Specific gravity is the ratio of the density of the material to that of water Pressure is force per unit area Pressure at a depth h is pgh External pressure applied to a confined fluid is transmitted throughout the fluid Summary of Chapter 10 Atmospheric pressure is measured with a barometer Gauge pressure is the total pressure minus the atmospheric pressure An object submerged partly or wholly in a fluid is buoyed up by a force equal to the weight of the fluid it displaces Fluid flow can be laminar or turbulent The product of the crosssectional area and the speed is constant for horizontal flow Where the velocity of a fluid is high the pressure is low and vice versa Backup 1010 Applications of Bernoulli s Principle from Torricelli to Airplanes Baseballs and TIA 139 Win A sailboat can move against the wind using the pressure differences on each side of the sail and using the keel to keep from going sideways Mainsail Copyright 2005 Pearson Prentice Hall1 Inc 1010 Applications of Bernoulli s Principle from Torricelli to Airplanes Baseballs and TIA A Home plate Copyright 2005 Pearson Prentice Hall Inc A ball s path will curve due to its spin which results in the air speeds on the two sides of the ball not being equal 1010 Applications of Bernoulli s Principle from Torricelli to Airplanes Baseballs and TIA A venturi meter can be used to measure fluid flow by measuring pressure differences Copyright 2005 Pearson Prentice Hall Inc 1010 Applications of Bernoulli s Principle from Torricelli to Airplanes Baseballs and TIA Air flow across the top helps smoke go up a chimney and air flow over multiple openings can provide the needed circulation in underground burrows Copyright 2005 Pearson Prentice Hall Inc 1011 Viscosity Real fluids have some internal friction called viscosity The viscosity can be measured it is found from the relation 3 l where n is the coefficient of viscosity F 77A 108 Moving plate V gt gt F gt Velocity i 3 gradient f Fluid Stationary plate Copyright 2005 Pearson Prentice Hall Inc 1012 Flow in Tubes Poiseuille s Equation Blood Flow The rate of flow in a fluid in a round tube depends on the viscosity of the fluid the pressure difference and the dimensions of the tube The volume flow rate is proportional to the pressure difference inversely proportional to the length of the tube and to the pressure difference and proportional to the fourth power of the radius of the tube 1012 Flow in Tubes Poiseuille s Equation Blood Flow This has consequences for blood flow if the radius of the artery is half what it should be the pressure has to increase by a factor of 16 to keep the same flow Usually the heart cannot work that hard but blood pressure goes up as it tries W5 Wall of quotI Artery wall thickening Blockage 39 ltagt V b l b Copyright 2005 Pearson Prentice Hall Inc 1013 Surface Tension and Capillarity The surface of a liquid at rest is not perfectly flat it curves either up or down at the walls of the container This is the result of surface tension which makes the surface behave somewhat elastically 1013 Surface Tension and Capillarity Soap and detergents lower the surface tension of water This allows the water to penetrate materials more easily more strongly N792 Water molecules are attracted to glass than Q they are to each other 1 just the opposite is true for mercury Water Mercury Copyright 2005 Pearson Prentice Hall Inc 1013 Surface Tension and Capillarity If a narrow tube is placed in a fluid the fluid will exhibit capillarity KJ k r h a 393 Glass tube Glass tube in water in mercury Copyright 2005 Pearson Prentice Hall Inc 1014 Pumps and the Heart This is a simple reciprocating pump If it is to be used as a vacuum pump the vessel is connected to the intake if it is to be used as a pressure pump the vessel is connected to the outlet ll in E Q l 4 Outl 39 39t Plston 39 1014 Pumps and the Heart a is a centrifugal pump b a rotary oilseal pump c a diffion pump 739 0mm Air diffuses into the oil jet Connection to container to 1 be evacuated Jet Mechanical Pump connection Copyright 2005 Pearson Prentice Hall Inc 1014 Pumps and the Heart The heart of a human or any other animal also L ft tquot ggm glggdy f 01333 gs operates as a pump 39 Mitral Tricuspid valve valve ventricle b ventncle Pulmonary artery to lun s Ri ht Aorta atrgigum Semilunar valves 39 Semilunar valves N quotquot Tr1cusp1d valve 0 d Copyright 2005 Pearson Prentice Hall Inc Mitral valve 1014 Pumps and the Heart In order to measure blood pressure a cuff is inflated until blood flow stops The cuff is then deflated slowly until blood begins to flow while the heart is pumping and then deflated some more until the blood flows freely Jacket Copyright 2005 Pearson Prentice Hall Inc Summary of Chapter 10 Where the velocity of a fluid is high the pressure is low and vice versa Viscosity is an internal frictional force within fluids Liquid surfaces hold together as if under tension
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