1stLaw-OPEN-Spring2010-7

# 1stLaw-OPEN-Spring20 - 1st Law Open System Reynolds Transport Theorem dB d ^ = dV(v rel n)dA dt CM dt CV CS Here B E = U 1 mv 2 2 E 1 v2 =e = u 2 m

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1st Law Open System • Reynolds Transport Theorem: Here: B: β : dB dt CM = d dt ρβ dV + ( v rel CS ˆ n ) CV dA E = U + mv 2 E m = e = u + v 2

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1st Law Open System LHS: Where: dB dt CM = dE dt CM = ˙ Q ˙ W tot ˙ Q = ˙ Q '' dA + ˙ q ''' ρ dV CV CS
1st Law Open System and: where: ˙ W tot = ˙ W body forces + ˙ W surface forces ˙ W body = ρ a v dV work done to system

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Assembling ˙ q ''' ρ dV + ˙ Q '' dA + a v ( ) dV W shaft p ( v ˆ n ) dA CS = CV CS CV d dt edV + e ( v ˆ n ) dA CS CV since (e + ) = ( h + v ) = h o ˙ Q ˙ W shaft + ( a v ) dV = d dt edV + h o ( v ˆ n ) dA CS CV CV
Simplifications No body forces • Uniform Flow: ˙ Q ˙ W shaft = d dt ρ edV + ˙ m h o out dV ˙ m h o in ˙ Q + ˙ m h o = in d dt E CV + ˙ W shaft + ˙ m h o out

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