485 Chapter 6 x Viscous Flow in Ducts 6.78 In Fig. P6.78 the connecting pipe is commercial steel 6 cm in diameter. Estimate the flow rate, in m3h, if the fluid is water at 20qC. Which way is the flow? Solution: For water, take U 998 kgm3 0.001 kgms. For commercial and P steel, take H | 0.046 mm, hence Hd 0.04660 | 0.000767. With p1, V1, and V2 all | 0, the energy equation between surfaces (1) and (2) yields 0 0 z1 | p2 0 z 2 h f , or h f Ug Guess turbulent flow: h f H d f 0.00767, guess ffully rough fbetter | 0.0204, Vbetter 2.50 L V2 d 2g Fig. P6.78 15 f 200000 | 5.43 m (flow to left) m 998(9.81) 50 V 2 0.06 2(9.81) § 0.1278 · | 0.0184, V | ¨ © 0.0184 ¸¹ 5.43, or: fV 2 | 0.1278 1/2 | 2.64 m , Re 158000 s m , Re better | 149700, f3rd iteration | 0.0205 (converged) s The iteration converges to f | 0.0205, V | 2.49 ms, Q (S4)(0.06)2(2.49) 0.00705 m3s 25 m3h m Ans. 6.79 A garden hose is used as the return line in a waterfall display at the mall. In order to select the proper pump, you need to know the hose wall roughness, which is not supplied by the manufacturer. You devise a simple experiment: attach the hose to the drain of an above-ground pool whose surface is 3 m above the hose outlet. You estimate the minor loss coefficient in the entrance region as 0.5, and the drain valve has a minorloss equivalent length of 200 diameters when fully open. Using a bucket and stopwatch, you open the valve and measure a flow rate of 2.0E4 m3/s for a hose of inside diameter 1.5 cm and length 10 m. Estimate the roughness height of the hose inside surface. Solution: First evaluate the average velocity in the hose and its Reynolds number: V Q A 2.0 E4 (S /4)(0.015)2 1.13 m , Red s UVd P 998(1.13)(0.015) 16940 (turbulent ) 0.001

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# 6.78 commercial steel 6 cm in diameter. Estimate