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HW2_SOLUTIONS(1) - ENU 4134 Homework Assignment#2 SOLUTIONS...

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ENU 4134 – Homework Assignment #2 SOLUTIONS – Fall 2011 – D. Schubring 1 ENU 4134 – Homework Assignment #2 SOLUTIONS – Fall 2011 a. Brief derivations and final equations used to evaluate all 5 components of pressure drop. 2 pts for each 2-phase term; 1 pt for each 1-phase term. NOTE: closed-form solutions were expected. If you saw an ugly integral in a 2-phase calculation and “punted” to a numerical solver, 1/2 each. Acceleration: Δ P acc = L boil 0 G 2 m vol fg dx dz dz (1) Δ P acc = L boil G 2 m vol fg dx dz (2) Friction (one-phase) – not really any derivation needed: f lo = 0 . 184 G m D μ f - 0 . 2 (3) Δ P fric, 1 - phase = f lo G 2 m L sub 2 rho f (4) Gravity (one-phase) – not really any derivation needed: Δ P grav, 1 - phase = L sub ρ f g (5) Friction (two-phase) Δ P fric, 2 - phase = L boil 0 f TP D G 2 m 2 ρ m ( z ) dz (6) Δ P fric, 2 - phase = f TP G 2 m 2 D L boil 0 1 ρ m ( z ) dz (7) Δ P fric, 2 - phase = f TP G 2 m 2 D L boil 0 x ρ g + 1 - x ρ f dz (8) Δ P fric, 2 - phase = f TP G 2 m 2 D L boil 0 z dx dz ρ g + 1 - z dx dz ρ f dz (9) Δ P fric, 2 - phase = f TP G 2 m 2 D L boil 0 z dx dz ρ g + 1 - z dx dz ρ f dz (10) Δ P fric, 2 - phase = f TP G 2 m 2 D z 2 dx dz 2 1 ρ g - 1 ρ f + z ρ f z = L boil z =0 (11) Δ P fric, 2 - phase = f TP G 2 m 2 D L 2 boil dx dz 2 1 ρ g - 1 ρ f + L boil ρ f (12) Δ P fric, 2 - phase = f TP G 2 m 2 D L 2
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