Question

QUESTION 6 (10 marks) Water needs to be transported between two settling ponds in a wastewater treatment facility, as illustrated in the diagram below. The surface of the second pond is 40m above the surface of the first pond. A pipe network connects the two ponds which consists of an entry, a wide open angle valve, four (4) 90° elbows with r/D = 2, a pump and an exit, and 150m of straight PVC pipe of diameter 177mm and dimensional roughness e = 0.0015mm. Find I i. an expression for the power required from the pump as a function of the volumetric flow rate, Q ii. The power required from the pump to maintain a flow rate of Q = 0.02m/s Pump H

Answer 1

Solution : friction head loss ht flv2 De Pump 40m Geiven, hength of the pipe h=150m diameter of pipe D = 177mm Roughness E = 0.0015 mm Kinematic vislokity of water v = 1.0533X16-6m2/A © let us assume required pump head obtained from Using Bernoulli equortton is top. Power of pump nghe (Potential Energy) pag hp (M = mast How rates) Expression for the power required by pump [P= PgQhp 2 Giyen, flow selle Q = 0.02 m3/A. 0.02 relocity of flow v= 0.8128 mis AX01772 4 Reynold number 0.0128X0.177 -= 136 500.69 (Tus bulent How) 1:0533 X10-6 friction factor, t= =)] 5.74 I en (3.71777 136588.690 friction factor If = 0.0160 0.01688 150X 0.81282 0.4796m 2x9.81X 0.177 - A Re=VD = 1-325 1.325 2 0.0015 In (3/Dt 5.74 Rog 2go

Minor Joss wetlicient for ongle valve kq=2 for 90 elbow with r/d=2, ke=0.2 to.sya Minor loss hm= 0.5Y²+2y2 29 + 4x0.2 x y2 ag hm = 3.8 X 0.01202 ag ag = 0.1279m 2x9:01 Now applying Bernoulli equatton between and Ⓡ, 4 + 4 g ta, the V23 that hift hm ng 26 t othp= 40 +0.4796 +0.1279 "PI = P2=Patm YI=82=0 2,20, Z2=40m 1hp=40-607m :: Power of pump required P= pga hp = 1000x9,0 1X 0.02 x 40.607 Power of pump required P = 7967.20 Watt