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Equations_Feb_20_2002_Class414

# Equations_Feb_20_2002_Class414 - Non-dimensionalization of...

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Non-dimensionalization of Momentum Equation 2 2 u y uu uvg ( T T ) xy ∂∂ += β + ν Introduce non-dimensional quantities with superscript *: ** o uuU ;xx L ; yy == = * L ) * s TT T ( T T ∞∞ =+ Note that all reference quantities are always dimensional. LHS: * * 00 o (u U ) v U uU (x L) (y L) + 0 22 UU uv LxLy RHS 2* * 0 s Uu gT( ) L 2 y β− + ν

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Divide LHS and RHS by 2 0 U L to obtain ** s 0 uu L uvg ( T T ) xy U ∂∂ += β * 2 T 2* 0 *2 22 0 UL u y LU * s 0L L1 g( T T ) T UR
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Equations_Feb_20_2002_Class414 - Non-dimensionalization of...

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