CheatSheet1 - ChBE 6200 Cheat Sheet Vector calculus...

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ChBE 6200 Cheat Sheet Vector calculus relationships: ~ ~ ~ ~ ~ ~ ~ ) ( C A B A C B A + = + ; ( 29 ~ ~ ~ ~ ~ ~ ~ C B C A C B A + = + ; ( 29 ( 29 ~ ~ ~ ~ ~ ~ C B A C B A = ; ( 29 ( 29 ~ ~ ~ ~ ~ ~ B A C B A C = i i b a b a = ~ ~ ; k j ijk b a b a e = × ~ ~ ; ij i T n T n = ~ ; j ij n T n T = ~ ; j i u x u = ~ ; j i x u u = ~ ; i i x u u = ~ Divergence theorem for a scalar Φ : Φ = Φ A V dA n dV ~ , vector ~ G : = A V dA n G dV G ~ ~ ~ and tensor T : = A V dA T n dV T ~ , where ~ n is the normal to the surface. Transport relationships: ( 29 Φ + Φ = Φ ~ v t Dt D , Φ scalar or vector, and ~ v is the fluid velocity. Reynolds Transport Theorem: ( 29 dA n v S dV t S dV Dt DS SdV Dt D Am Vm Vm Vm + = = ~ ~ Unidirectional Flow:
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CheatSheet1 - ChBE 6200 Cheat Sheet Vector calculus...

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