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HW_26_Soln

# HW_26_Soln - ME 309 Fall 2008 Section 2(Merkle Homework 25...

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ME 309 Fall 2008 Section 2 (Merkle) Homework # 25 Due Fri 1 Nov 2008 Problem 26-1 . Methanol at 300 K ( ρ = 788.4, μ =.5.857e-4) flows through a 40 mm pipe and is measured by an orifice meter with a 30 mm diameter orifice that is equipped with corner taps. The differential pressure is measured by a mercury ( ρ = 13,600) manometer as 110 mm . Find the mass flow rate of methanol and the average velocity. Solution: Given: density of working fluid and manometer fluid, height difference in manometer, pipe and orifice diameters, corner taps Find: flow rate and average velocity Assumptions: steady, fully developed flow Constant properties Incompressible fluid Analysis: Calculate pressure drop across taps: ( ) ( ) Pa h g p p meth Hg 820 , 13 110 . 0 * 807 . 9 * 4 . 788 600 , 13 * * 2 1 = - = Δ - = - ρ ρ Discharge coefficient for corner tap/orifice plate: 2 75 . 0 5 . 2 8 1 . 2 Re * 71 . 91 * 184 . 0 * 0312 . 0 5959 . 0 D d C β β β + - + = Calculate beta: 75 . 0 / = = D d β A_t = pi*d*d/4. =pi*0.03*0.03/4 = 0.000707 Calculate flow rate: ( ) ( ) 4 2 1 1 1 1 * 2 β ρ ρ ρ - - = = meth t d t t meth meth p p A C A u u A Equations for Cd and velocity are coupled. Need to find Cd first, but can’t find without ReD—Guess a value for Cd, calculate velocity, then Re and update Cd with Re value. Repeat.) Guess Cd = 0.9 Calculate flow rate: ( ) ( ) s m p p C u meth d / 35 . 1 ) 4 ^ 75 . 0 1 ( * 4 . 788 13820 * 2 * 2 ^ 75 . 0 * 9 . 0 1 / 2 4 2 1 2 1 = - = - - = β ρ β 4 26 . 7 4 857 . 5 04 . 0 * 35 . 1 * 4 . 788 Re e e d = - = Calculate Cd from formula: Cd = 0.5945. Put Cd = 0.5945 back in and recompute again—

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( ) ( ) s m p p C u meth d / 895 . 0 ) 4 ^ 75 . 0 1 ( * 4 . 788 13820 * 2 * 2 ^ 75 . 0 * 5945 . 0 1 / 2 4 2 1 2 1 = - = - - = β ρ β 4 82 . 4 4 857 . 5 04 . 0 * 895 . 0 * 4 . 788 Re e e d = - = Calculate Cd from formula: Cd = 0.5945. Same as before Final solution: u = 0.895m/s Flow rate: s kg uA m / 887 . 0 4 / 2 ^ 04 . 0 * * 895 . 0 * 4 . 788 = = = π ρ &
Problem 26-2. a)

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