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p250c14:1Chapter 15: FluidsFluids: substances which flowLiquids: take the shape of their container but have a definite volumeGases: take the shape and volume of their containerDensitywatertorelativedensity =gravity specific10001: :units SI333mKgcmgnotemKgVolumeMassDensityVm===ρSubstance Mass density ρ (kg/m3) Hydrogen Helium Air water alchohol gasoline balsa wood pine aluminum iron gold lead 0.09 0.18 1.30 1000 790 680 130 370 2700 7800 19000 11000p250c14:2Pressure in a fluid: force per area P = F/AForce = normal force, pressure exerts a force perpendicular to the surface.pressure of the bottom of a container on a liquid balances the pressure the liquid exerts on the container bottomUnits for pressure:1 N/m2 = 1 Pa1 Bar = 105 Pa ~ atmospheric pressure (14.7 psi)*1 atmosphere = 1.01 E5 Pa1 mm Hg = 1.33E2 Pa1 torr = 1.33E2 Pa1 lb/in2 (psi) = 6.89 E3 Pa *atmospheric pressure varies from .970 bar to 1.040 barp250c14:3Example: find the pressure exerted on the skin of a balloon if you press with a force of2.10 N using y6our fingertip (area = 1.00E-4 m2) or a needle ( area = 2.50E-7 m2) . Compare these answers with the pressure needed to pop the balloon, 3.0E5 N/m2.p250c14:4Most pressure gages detect pressure differences between the measured pressure and a reference pressure.absolute pressure: the actual pressure exerted by the fluid.gauge pressure: the difference between the pressure being measured and atmospheric pressure.Pg = P - Pat Some important aspects of pressure in a fluidThe forces a fluid at rest exerts on the walls of its container (and visa versa) always perpendicular to the walls.An external pressure exerted on a fluid is transmitted uniformly throughout the volume of the fluid.The pressure on a small surface in a fluid is the same regardless of the orientation if the surface.p250c14:5Example: A flat roof of a house is 10.0 m by 8.0 m, and has a mass of 7500kg. Just before a severe storm the windows of the house are shut so tightly that the air pressure inside remained at 1.013 bars even when the out side pressure fell to .980 bars. Compare the net force on the house due to the difference in pressure to the weight of the roof. (this is not in book, but is more interesting...)p250c14:6Static Equilibrium in Fluids: Pressure and DepthA fluid supports itself against its weight with pressure.The fluid also must support itself against external pressureP = F/A = Pat + weight of fluidw = mg = ρ Vg V = AhP = Pat + ρghGeneralizing P2 = P1 + ρghhAPatPAP1P2hp250c14:7Example: A box 20 cm on a side sits in an unknown fluid. The pressure at the top of the box is 105.0 kPa and the pressure at the bottom of the box is 106.8 kPa. What is the density of the fluid?p250c14:8pF1 = PA1F2 = P A2Pascal’s Principle: The external pressure applied at one point in an enclosed fluid is transmitted to every part of the fluid and to the walls of the container.Application: HydraulicsBuoyant force: pressure balances gravity for a fluid to support itself.Fnet,pressure = w = ρVgFnet = ρfluidVgArchimedes’ principle:Buoyant force = weight of fluid displacedFb = Vρgp250c14:9Example: A piece of wood with a density of 706 kg/m3 is tied to a string to the bottom of a water filled flask. The wood is completely submerged, and has a volume of 8.00E-6 m3. What is the tension in the string? If the string is released so that the block floats to the surface, how much of the block remains below the surface (volume).p250c14:10Fluid Flowwith approximations:incompressible fluid no viscosity (friction)laminar flow (a.k.a. streamline flow)in contrast with turbulent flow(the rate of flow is volume per time)A Avt∆V = Av∆tp250c14:11If no fluid is added/lost, flow rate must be the same throughout∆min= ρ2v1A1∆tmin = moutρ1v1A1∆t = ρ2v2A2 ∆tincompressible fluid: ρ2 = ρ2 Equation of Continuity: v1A1 = v2A2 ∆mout= ρ2v2A2∆tp250c14:12Example: Water travels through a 9.60 cm diameter hose with a speed of 1.3 m/s. At the end of the hose, the water flows out through a nozzle whose diameter is 2.50 cm. What is the speed of the water as it leaves the nozzle?p250c14:13Bernoulli’s Equation: flow with changing heights and pressureWork-Energy Theorem + incompressible fluidA2y1y2A1p1, v1p2, v2122112222122222111221121212121mgymgyPEvVvVmvmvKEtvAptvApxFxFWKEPEW−=∆−=−=∆∆−∆=−=∆∆+∆=∆ρρ222221112121vgypvgyp ρρρρ ++=++p250c14:14Applications of Bernoulli’s EquationLiquid at rest:P2 − P1 = ρ g(y1 − y2 ) old news!!!No pressure difference, one part “at rest”:Torricelli’s theoremtypically atmospheric pressure for bothApplication/Demonstration: Bernoulli Strips222221112121vgypvgyp ρρρρ ++=++vhghvvgh22122== ρρp250c14:15A bucket filled with water has a hole in the side, 0.150 m below the water level. How far to the side will the water hit the ground if the hole is 0,500 m above the ground


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PSU PHYS 250 - Fluids substances

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