Question

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June 1. Consider steady, fully-developed laminar flow of air through a Laminar Flow Element (LFE, a type of flow-meter) with an aligned bundle of 100 small bore tubes, each of diameter D 2.00 mm, and length L 200.0 mm. The pressure drop per unit length (Ap/L) across each of the 100 tubes is a function of the tube diameter D, fuid viscosity u (in units N s/m2), and average air velocity Vave. a) Find the dimensionless Pi group(s). b) For a measured pressure drop of Ap 450 N /m2, the total volumetric flow-rate through (all 100 tubes of) the LFE is 0.00491 m3/ s. Calculate the volumetric flow-rate through the LFE for a measured pressure drop of Ap = 550 N /m2.

Answer 1

= f( AP D, V F( AP D u, V L dimension 0f each tern lustiaM AP 2 ML T L ME T LT L L

voruable 5 = 3 Vorial le in dimension pie (A term) 5-3 2 ho Repeating asucle as Taking D, u, V a 2 AP ariHing MLT ML'T"] dimensions For b1 [LT'] ai- bi+Ct1 [-"ן +iיה. bl. MOLT MT Companing spanding CoYTes M, Land T Power -bt-C o ai-bi + 1 =0 ai-1 FoY 2 a2 MOLT b2t1 M] a2-b2C21 b2 C22 [rj b2t10 b2=-1

- b2-S2- 2 = 0 C2-(-) 2 = 1-2 = -1 a2-b2t C) - 1 O 1 1 -1= 0 g a21 D.VP D 4 P 2 V쓰 04 P F(K 2) V씨L、 K AP D 2 ΔP OY D2. Ap D2 4 p o D 4 A Pr Q2

O 0049 X 5 50 450 Q2 2