Aero II 39 Review of Fluid Theory

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Aero II 39 Review of Fluid Theory
J. E. Brandenburg EAS 3010 Spring 2007
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Agenda

• Review of Incompressible Viscous Flow

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Vortex
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Vortex
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Vortex
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Circulation
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Bernoulli Equation
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Vortex Ring Shooter
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Downwash
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Review of Fluid Theory
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Molecular Theory of Gases
Ideal Gas law P nkT n molecules per unit
volume kT ? average kinetic energy per molecule
lt1/2 mVth2 gt
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Continuity Equation
 
l     
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Continuity Equation Cont.
which becomes as ? x ? 0.
 
l      Similar analysis can be done for the
fluxes across the other four faces to yield the
continuity equation, which can also be written
as .
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Continuity
Water flow speeds up in smaller pipe nozzle flow
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Force per unit volume without viscosity
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Momentum Equation
High pressure gas
Expanding Gas flow
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Incompressibility Condition
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Incompressibility Condition
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Energy Equation without viscosity
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Energy Equation cont.
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Force on a fluid Element in Viscous flow
No point torques allowed
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Turbulent Transition
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Reynolds Number
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Transition to turbulence
At Re gt40000 flow in water pipe becomes turbulent
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Viscosity in a Gas
?
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Viscosity Cont.
Downward flux of y momentum
Net flux
?
Upward flux of y momentum
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Viscosity Cont.
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Laminar versus Turbulent flow
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The Boundary Layer
Re??VL/?
L
L
Near surface viscous effects create a boundary
layer that grows with distance and Reynolds
number grows also
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Turbulent Transition on a wing
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Turbulent Transition
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Mars Hurricane
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Great Red Spot- Jupiter