Chapter 15: Fluids. Mass Density = Volume. note : Fluids: substances which flow

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1 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 = Volume Kg SI units : 3 m note : g Kg = cm m specific gravity = density relative to water Substance Hydrogen Helium Air water alchohol gasoline balsa wood pine aluminum iron gold lead Mass density ρ (kg/m 3 ) p50c4:

2 Pressure in a fluid: force per area P = F/A Force = 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 bottom Units for pressure: N/m = Pa Bar = 0 5 Pa ~ atmospheric pressure (4.7 psi)* atmosphere =.0 E5 Pa mm Hg =.33E Pa torr =.33E Pa lb/in (psi) = 6.89 E3 Pa *atmospheric pressure varies from.970 bar to.040 bar p50c4:

3 Example: find the pressure exerted on the skin of a balloon if you press with a force of.0 N using y6our fingertip (area =.00E-4 m ) or a needle ( area =.50E-7 m ). Compare these answers with the pressure needed to pop the balloon, 3.0E5 N/m. p50c4:3

4 Most 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. P g = P - P at Some important aspects of pressure in a fluid The 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. p50c4:4

5 Example: A flat roof of a house is 0.0 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.03 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...) p50c4:5

6 Static Equilibrium in Fluids: Pressure and Depth A fluid supports itself against its weight with pressure. P at The fluid also must support itself against external pressure P = F/A = P at + weight of fluid h w = mg = ρ Vg V = Ah P A P = P at + ρgh Generalizing P = P + ρgh P h P A p50c4:6

7 Example: A box 0 cm on a side sits in an unknown fluid. The pressure at the top of the box is 05.0 kpa and the pressure at the bottom of the box is 06.8 kpa. What is the density of the fluid? p50c4:7

8 Pascal 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: Hydraulics F = PA F = P A p Buoyant force: pressure balances gravity for a fluid to support itself. F net,pressure = w = ρvg F net = ρ fluid Vg Archimedes principle: Buoyant force = weight of fluid displaced F b = Vρg p50c4:8

9 Example: A piece of wood with a density of 706 kg/m 3 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 m 3. 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). p50c4:9

10 Fluid Flow with 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) V = Av t A A vt p50c4:0

11 If no fluid is added/lost, flow rate must be the same throughout m in = ρ v A t m out = ρ v A t m in = m out ρ v A t = ρ v A t incompressible fluid: ρ = ρ Equation of Continuity: v A = v A p50c4:

12 Example: Water travels through a 9.60 cm diameter hose with a speed of.3 m/s. At the end of the hose, the water flows out through a nozzle whose diameter is.50 cm. What is the speed of the water as it leaves the nozzle? p50c4:

13 Bernoulli s Equation: flow with changing heights and pressure Work-Energy Theorem + incompressible fluid A p, v y p, v y A W W KE PE = PE + KE = F x F x = p A v t p = mv mv = ρvv ρvv = mgy mgy A v t p + ρ gy + ρv = p + ρgy + ρv p50c4:3

14 Applications of Bernoulli s Equation p + ρ gy + ρv = p + ρgy + Liquid at rest: P P = ρ g(y y ) ρv old news!!! No pressure difference, one part at rest : Torricelli s theorem ρgh v = = ρv gh h v typically atmospheric pressure for both Application/Demonstration: Bernoulli Strips p50c4:4

15 A bucket filled with water has a hole in the side, 0.50 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 level? p50c4:5

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