ch97 - FLOW IN A CONSTANT-AREA DUCT WITH FRICTION (not...

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FLOW IN A CONSTANT-AREA DUCT WITH FRICTION (short ducts/pipes; insulated ducts/pipes) (not isentropic, BUT constant area, adiabatic)
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Constant Area Duct Flow with Friction Quasi-one-dimensional flow affected by: no area change, friction , no heat transfer, no shock friction
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C O N S T A N T A R E A F R I C T I O N CH A D I A B A T I C 12.3 Governing Euations • Cons. of mass • Cons. of mom. • Cons. of energy • 2 nd Law of Thermo. (Ideal Gas/Const. c p ,c v ) Eqs. of State • p = ρ RT • h 2 -h 1 = c p (T 2 – T 1 ) Δ s = c p ln(T 2 /T 1 ) - Rln(p 2 /p 1 ) {1-D, Steady, F Bx =0 only pressure work}
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Quasi-One-Dimensional, Steady, F Bx = 0, dW s /dt = 0, dW shear /dt = 0, dW/dt other = 0, effects of gravity = 0, ideal gas, c v , c p is constant Property relations for ideal gas with c v and c p constant Cons. Of Mass Cons. of Momentum Cons. of Energy 2 nd Law of Thermodynamics
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+ constant area , adiabatic = Fanno Flow A 1 = A 2 R X only friction No δ Q/dm term
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Constant area, adiabatic but friction If know: p 1 , ρ 1 , T 1 , s 1 , h 1 , V 1 and R x Can find: p 2 , ρ 2 , T 2 , s 2 , h 2 , V 2 properties changed because of R x
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(T-s curve)
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T-s diagram for Fanno Line Flow s 2 -s 1 = c p ln(T 2 /T 1 ) – Rln(p 2 /p 1 ) p = ρ RT; p 2 /p 1 = ρ 2 T 2 /( ρ 1 T 1 ); R = c p -c v s 2 -s 1 = c p ln(T 2 /T 1 ) – Rln(p 2 /p 1 ) = c p ln(T 2 /T 1 ) – [ R ln( ρ 2 / ρ 1 ) + ( c p -c v )ln(T 2 /T 1 )] = – Rln( ρ 2 / ρ 1 ) + c v ln(T 2 /T 1 ) ρ 2 V 2 = ρ 1 V 1 ; ρ 2 / ρ 1 = V 1 /V 2 s 2 -s 1 = c v ln(T 2 /T 1 ) – Rln(V 1 /V 2 )
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s 2 -s 1 = = c v ln(T 2 /T 1 ) – Rln(V 1 /V 2 ) Energy equation (adiabatic): h + V 2 /2 = h o ; V = (2[h o – h]) 1/2 p ; h = c p T V = (2c p [T o – T]) 1/2 -ln[V 1 /V 2 ] = -(1/2)ln[(T o -T 1 )/(T o -T 2 )] = (1/2)ln[(T o -T 2 )/(T o -T 1 )] s 2 -s 1 = c v ln(T 2 /T 1 ) + ½Rln [(T o -T 2 )/(T o -T 1 )] ( p to ρ to V to T)
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T 1 , s 1 , V 1 , … Locus of possible states that can be obtained under the assumptions of Fanno flow: Constant area Adiabatic ( h o = h 1 +V 1 2 /2 = c p T o ) x T o s - s 1 = c v ln( T/ T 1 ) + ½Rln [( T o -T 2 )/( T o - T 1 )]
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C O N S T A N T F R I C T I O N CH TS curve properties A D I A B A T I C 12.3 A R E A direction ?
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Note – can only move from left to right because s 2 > s 1
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This note was uploaded on 04/26/2010 for the course MAE 101B 101B taught by Professor Rohr during the Summer '09 term at UCSD.

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ch97 - FLOW IN A CONSTANT-AREA DUCT WITH FRICTION (not...

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