Question

Chapter 08, Problem 044 A 3-ft-diameter duct is used to carry ventilating air = 2.373 x 10- slugs/fr", v= 1.57 x 10 ft/s) into a vehicular tunnel at a rate of 8000 ft/min. Tests show that the pressure drop is 1.1 in. of water per 1500 ft of duct. What is (a) the value of the friction factor for this duct and (b) the approximate size of the equivalent roughness of the surface of the duct? Use this figure. (a)f= (b) = Show Work is REQUIRED for this question: Modify Show Work

Answer 1

Congider the duct is Horizontal. Applying Bernoull's theorem at inlet & exiti PL + V2 + 2,= Pz + Vz? +22+f alo 23 ile Since 2,5 Zz 4 V, vz | .: P4-6 = x (filos) – 0 Given that the pressure drop is 1-1 in. Pq - Pz = razoxh = 82-41b/ft3 × 1.2/12 24 = 624 44t2 = 5.72 66644 V= 0% = Svou ft/min * lmin/sos 1/4 * ( 38+)2 V = 18.86 dt1s ... from egh Oi.. f = 2D (R-P2) el v2

f = 2* ( 3 ft) x ( 5-72 16/772) (2-373 x 103 Slug(43) * (1500 ft) * (18.86)2147,2 f = 0.0271 0.0271 An Reynalds number! - Re = V0 - 18.86 St's x 347 1-57% 164f+45 Re = 360382 = 3-6* 105 From fig. for f = 0.027) Re = 3-6 x 105 f = 0.00377 s . .: E = 0.0037* ( 3 ft) E = 0.0111 ft