Intro-FM-2009 - IntroductiontoFluidMechanics Fred Stern,...

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57:020 Fluid Mechanics 1 Introduction to Fluid Mechanics CFD EFD AFD 2 0 1 Re i j D p u u Dt ∇• = = -∇ + +∇ • U U U Fred Stern, Tao Xing, Jun Shao, Surajeet Ghosh, Shanti Bhushan 8/27/2009
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57:020 Fluid Mechanics 2  Fluid Mechanics Fluids essential to life Human body 65% water Earth’s surface is 2/3 water Atmosphere extends 17km above the earth’s surface History shaped by fluid mechanics Geomorphology Human migration and civilization Modern scientific and mathematical theories and methods Warfare Affects every part of our lives
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57:020 Fluid Mechanics 3 History Faces of Fluid Mechanics Archimedes (C. 287-212 BC) Newton (1642-1727) Leibniz (1646-1716) Euler (1707-1783) Navier (1785-1836) Stokes (1819-1903) Reynolds (1842-1912) Prandtl (1875-1953) Bernoulli (1667-1748) Taylor (1886-1975) Kolmogorov (1903-1987)
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57:020 Fluid Mechanics 4 Significance Fluids omnipresent Weather & climate Vehicles: automobiles, trains, ships, and  planes, etc. Environment Physiology and medicine Sports & recreation Many other examples!
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57:020 Fluid Mechanics 5 Weather & Climate Tornadoes Hurricanes Global Climate Thunderstorm
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57:020 Fluid Mechanics 6 Vehicles Aircraft Submarines High-speed rail Surface ships
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57:020 Fluid Mechanics 7 Environment Air pollution River hydraulics
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57:020 Fluid Mechanics 8 Physiology and Medicine Blood pump Ventricular assist device
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57:020 Fluid Mechanics 9 Sports & Recreation Water sports Auto racing Offshore racing Cycling Surfing
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57:020 Fluid Mechanics 10 Fluids Engineering 
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57:020 Fluid Mechanics 11 Analytical Fluid Dynamics The theory of mathematical physics  problem formulation Control volume & differential analysis Exact solutions only exist for simple  geometry and conditions Approximate solutions for practical  applications Linear Empirical relations using EFD data
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57:020 Fluid Mechanics 12 Analytical Fluid Dynamics Lecture Part of Fluid Class Definition and fluids properties Fluid statics Fluids in motion Continuity, momentum, and energy principles Dimensional analysis and similitude Surface resistance Flow in conduits  Drag and lift
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57:020 Fluid Mechanics 13 Analytical Fluid Dynamics Schematic Example: laminar pipe flow Exact solution  : 2 2 1 ( ) ( )( ) 4 p u r R r x μ = - - Friction factor: 8 8 64 Re 2 2 w du dy w f V V τ ρ = = = Assumptions:  Fully developed, Low  Approach : Simplify momentum equation,   integrate, apply boundary conditions to  determine integration constants and use  energy equation to calculate head loss x g y u x u x p Dt Du + + + - = 2 2 2 2 Head loss: 1 2 1 2 f p p z z h γ + = + + 2 2 32 2 f L V LV h f D g D = = UD 2000 Re ρ < μ = 0 0 0
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57:020 Fluid Mechanics 14 Analytical Fluid Dynamics Example: turbulent flow in smooth pipe(             ) 0 5 y + < < 1 ln u y B κ + + = + 5 20 10 y + < < * 0 1 U u r f u r   - = -  ÷   5 10 y + u y + + = ( 29 ( 29 * 0 * 1 ln u r r r u B
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This note was uploaded on 12/08/2011 for the course MECHANICS 57:020 taught by Professor Fredrickstern during the Fall '10 term at University of Iowa.

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Intro-FM-2009 - IntroductiontoFluidMechanics Fred Stern,...

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