Ch15 - Chapter 15: Fluid Motion Fluids Characteristics of...

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Chapter 15: Fluid Motion Fluids ± Characteristics of fluids • Microscopically molecules of a fluid do not have long-range order. But liquids do have short-range order unlike gases • Fluids can flow and conform to the boundaries of a container • Fluids cannot sustain a shearing stress
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Fluids (cont’d) ± Some useful quantities m ² Density for ,volume V mass V m V m = = ρ for uniform solid or liquid unit kg/m 3 (at STP for a gas) in SI unit 3 3 3 kg/m 2 . 1 ; kg/m 10 0 . 1 = × = air water 3 3 3 3 kg/m 10 35 . 11 ; kg/m 10 1 . 0 × = × = lead styrofoam ² Pressure for area A and normal force F dA dF A F p A = 0 2 m 1 / N 1 Pa = in SI unit unit pascal other useful units: 2 5 in / lb 7 . 14 torr 760 Pa 10 01 . 1 atm 1 = = × = height of a column of Hg corresponding to this pressure (mm)
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Pressure ± Pressure of a liquid at rest (uniform density) A A 2 y 1 y fluid level imaginary box 2 F 1 F mg A p F 1 1 = A p F 2 2 = 0 ) ( 1 2 2 1 = + gA y y F F ρ weight of the imaginary box hg g y y p p = = ) ( 1 2 1 2 mg h hg p p + = 1 2
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Pressure (cont’d) ± Pressure of a fluid at rest : gauge pressure hg p p ρ + = 1 2 atmospheric pressure 0 p gauge pressure: A A 2 y 1 y fluid level imaginary box 2 F 1 F mg h gauge gauge p p p p p p 2 0 2 1 0 1 + = + = atmospheric pressure
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A simple model for atmospheric pressure ± Pressure of a gas at rest ( ) kp = ρ gdy y y g p p dp = = = ) ( 2 1 1 2 , 0 , 1 2 1 2 y y p p When kpgdy gdy dp = = kpg dy dp = / ) ( 1 2 1 2 y y kg e p p =
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Barometer ± Pressure measurement using a liquid: ( measures absolute pressure ) h 0 = p 0 p atmospheric pressure From ) ( 2 1 1 2 y y g p p + = ρ as 0 1 2 2 , , 0 p p h y p = = = gh p = 0 If the liquid is mercury, for 1 atm : m/s 83 . 9 , kg/m 10 6 . 13 , Pa 10 3 . 101 atm 1 3 3 3 0 = × = × = = g p Hg mm 760 m 758 . 0 / 0 = = g p h
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Manometer ± Pressure measurement using a liquid : ( measures gauge pressure ) g p h 0 p level 1 level 2 ) ( 2 1 1 2 y y g p p + = ρ 0 , , , 1 0 1 2 2 = = = = y p p h y p p gh p p p g = = 0 gauge pressure liquid tank manometer
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Pascal’s law ± Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and walls of the containing vessel piston weight liquid P h ext p p (area A) gh p p p ext ρ + + = 0 pressure at P pressure due to weight w: w/A atmospheric pressure w pressure due to liquid above P incompressible ext p p =
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Pascal’s law (cont’d) ± Hydraulic lever 2 2 1 1 / / A F A F p = = 1 x 2 x 1 F 2 F 1 A 2 A 1 1 2 2 ) / ( F A A F = 1 2 1 2 1 / F F A A > > 1 2 1 2 2 2 1 1 ) / ( x A A x A x A x = = 1 1 1 1 2 1 1 1 2 2 2 2 ) / ( ) / ( W x F x A A F A A x F W = = = =
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Buoyancy ± Origin of buoyancy • Consider a submerged massless object filled with the same fluid as the fluid that surrounds the object 1 P 2 P 1 F 2 F 0 ) ( 1 2 = = g m
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Ch15 - Chapter 15: Fluid Motion Fluids Characteristics of...

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