examf - EGN3353C Fluid Mechanics Spring 2010 Final Exam...

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LAST NAME:___________________________ FIRST NAME:________________ SECTION:______ INSTRUCTIONS: Closed book, closed notes, calculator allowed. EGN3353C Fluid Mechanics Spring 2010 Final Exam Formula Sheet Energy Equation Control-volume form ˙ Q net in + ˙ W shaft , net in = d dt CV ρ e d + CS p ρ + u + V 2 2 + gz ρ V r · n dA. (1) For steady flow, evaluating control-surface integral for single inflow and outflow gives ˙ Q net in + ˙ W shaft , net in = ˙ m p out ρ out p in ρ in + u out u in + V 2 out V 2 in 2 + g ( z out z in ) . (2) Energy-density form [J/kg]: q net in + w shaft , net in = p out ρ out p in ρ in + u out u in + V 2 out V 2 in 2 + g ( z out z in ) . (3) Head form [m]: w shaft , net in g + p in ρ in g + V 2 in 2 g + z in = p out ρ out g + V 2 out 2 g + z out + h L , (4) where h L is the head loss h L = u out u in q net in g . (5) Isentropic Flow Subscript 0 and superscript denote stagnation (total) and sonic conditions, respectively T 0 T = 1 + γ 1 2 M 2 (6) p 0 p = T 0 T γ γ 1 = 1 + γ 1 2 M 2 γ γ 1 (7) ρ 0 ρ = T 0 T 1 γ 1 = 1 + γ 1 2 M 2 1 γ 1 (8) A A = 1 M 2 γ + 1 1 + γ 1 2 M 2 γ +1 2( γ 1) (9) ˙ m = ρ uA = ρ a A = 2 γ + 1 γ +1 2( γ 1) p 0 γ RT 0 A (10) Normal Shock Waves Subscripts 1 and 2 denote conditions ahead of and behind the shock wave, respectively ρ 2 ρ 1 = u 1 u 2 = ( γ + 1) M 2 1 2 + ( γ 1) M 2 1 (11) p 2 p 1 = 1 + 2 γ γ + 1 M 2 1 1 (12) M 2 = 2 + ( γ 1) M 2 1 2 γ M 2 1 ( γ 1) (13)
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EGN3353C Fluid Mechanics Spring 2010
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