{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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—
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
( ) ( ) 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 &
Background image of page 2
Problem 26-2. a)
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}