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Lecture_Note_Ch_2

Lecture_Note_Ch_2 - ME 342 Fluid Mechanics Lecture Note on...

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Lecture Note on Ch. 2: Pressure Distribution in a Fluid Prof. Chang-Hwan Choi Stevens Institute of Technology Department of Mechanical Engineering ME 342 Fluid Mechanics Spring 2008

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Motivation • Hydrostatic condition: zero fluid velocity Æ Pressure variation is due only to the weight of the fluid. – Pressure distribution in the atmosphere and the oceans – Design of manometer pressure instruments – Forces on submerged flat and curved surfaces – Buoyancy on a submerged body – Behavior of floating bodies • Fluid moving in rigid-body motion: e.g., a spinning tank of liquid • Pressure measurement instruments Roosevelt Dam in Arizona. Hydrostatic pressure, due to the weight of a standing fluid, can cause enormous forces and moments on large-scale structures such as a dam.
Pressure and Pressure Gradient volume unit per force net : press press f f k j i F , , p dxdydz z p y p x p d dxdydz z p dF dxdydz y p dF dxdydz x p dydz dx x p p pdydz dF z y x −∇ = = = = = + = Equilibrium of a small wedge of fluid at rest. Net x force on an element due to pressure variation. n. orientatio of t independen property, point a is fluid static a in Pressure , If p p p p p z z g p p p p F F n z x n z n x z x = = = + = = = Σ = Σ 0 2 1 , : 0 , 0 ρ

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Equilibrium of a Fluid Element • Gage and Vacuum Pressures 1. p > p a : Gage pressure Æ p (gage) = p p a 2. p < p a : Vacuum pressure Æ p (vacuum) = p a p Illustration of absolute, gage, and vacuum pressure readings.
Hydrostatic Pressure Distributions head pressure or : Liquids 0) 0, (with visc visc visc grav press : ) ( ) ( 1 2 2 1 1 2 1 2 1 2 2 1 1 2 γ ρ p p p z z z z p p z z dz p p g dz dp g p p = = = = = = = = = = = + + −∇ = + + = Σ k g f a g a f g f f f f Hydrostatic-pressure distribution: p a = p b = p c = p d ; p A = p B = p C p D Hydrostatic-pressure distribution in oceans and atmospheres.

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The Mercury Barometer mercury? of instead used is water if What m N/m Pa, 101,350 standard, level - sea At 3 761 . 0 100 , 133 ) 0 ( 0 ) ( 1 2 1 2 = = = = = = h p p h h p z z p p M a M a M a γ A barometer measures local absolute atmospheric pressure. The height of a mercury column is proportional to p atm .
Hydrostatic Pressure in Gases • Gases are compressible Æ Density is not a constant. ) 1 ) 00650 . 0 ) ( exp ln 1 2 1 2 2 1 2 1 1 2 air (for 5.26 , , K/m 288.16K, ( If ), atmosphere l (isotherma If 0 0 0 0 0 = = = = = = = = = = = ∫∫ RB g T Bz p p B T Bz T T RT z z g p p T T T dz R g p p p dp g RT p g dz dp RB g a ρ Temperature and pressure distribution in the U.S. standard atmosphere.

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