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Lecture_19_notes - Chemical Engineering 374 Fluid Mechanics...

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1 1 Chemical Engineering 374 Fluid Mechanics Fall 2011 Single Pipelines Pipelines with friction losses 2 Δ P ρ + Δ v 2 2 + g Δ z = ˙ W u ˙ m - ˙ F ˙ m Δ P ρ + Δ v 2 2 + g Δ z = - fLv 2 2 D - Kv 2 2 Ignoring the Work Term: - F (= - ˙ F/ ˙ m ) One equation in One Unknown Pick Two Points Carefully
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2 Problem Types Types I and IV are easy. Types II, III require iteration Parameters: Δ P, L, D, V, μ, ρ , ε Equations: Re = ρ Dv/ μ f=f(Re, ε /D) Δ P = fL ρ v 2 /2D 3 Problems I, II, III from Swamee-Jain Relations See Book Page 380 Type I Procedure Re = ρ Dv/ μ f=f(Re, ε /D) Δ P = fL ρ v 2 /2D 4 Find Pressure Drop Solve Re from (1) Solve f from Colbrook Eqn. (2) etc. Solve Δ P from (3)
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3 Type II Procedure Re = ρ Dv/ μ f=f(Re, ε /D) Δ P = fL ρ v 2 /2D 5 Find Flow Rate (velocity) Implicit: v appears in (1), (2), (3) Iterate (several ways) 1. Guess f as fully turbulent (where Moody levels off) 2. v from (3) 3. Re from (1) 4. f from (2) 5. Repeat to convergence 1. Guess Re 2. Compute f from (2) 3. v from (3) 4. Re from (1) 5. Repeate OR Type III Procedure Re = ρ Dv/ μ f=f(Re, ε /D) Δ P = fL ρ v 2 /2D 6 Find Pipe Diameter Implicit: D appears in (1), (2), (3) Iterate (several ways): 1. Guess D 2. Re from (1) 3. f from (2) 4. D from 3 5. Repeate
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