Question

Water is supplied at a rate of 100 ft? 5-1, pressure of 50 psi to a turbine through a 5 ft 2 cross-sectional area pipe. The exit conditions are: Water discharges through a pipe of cross-sectional areas 2 ft2 into the atmosphere. The turbine develops a power of 500 hp. The total head loss in this system is 10ft. Assume density of water is 62.8 lbf/m3 Part 1: The velocity with which waters discharges into the atmosphere is ft s-1 Part 2: The efficiency of the turbine is Part 3: If the turbine operates at 100% efficiency, to extract the same amount of power, the pressure at which water is supplied is psi

Answer 1

Solution Data giveny Flow Rate (Q) = loott/ Pressure (P) = 50psi = 7200 16/6 Area (All= 5H² A₂ = 2ft² Pe=0 P = 50oh e a coche he head loss ha=lott 22 B 62-8 lb, 1 kB 6 Velocity at discharge (Ve) = 0 / 100 = 50ft/s eyer Velocity at inlet (V)- 100 =2044/5 2 energy per unit weight of water at inlet & +zi e, = 120.ght energy at outlet 12 W, Turbine work la = 39.06 ft Energy balance e, = WI + C, the

- WT I = e, -le-hg = 120.9-39.06-10=71-83 ft mg - WT = 1890) 71.83 = 62.88 100x71.83 x= 451139.5 lb.ft I botter - Śso hp - (W x = 820.25 hp efficiency (W) = 2 2 2 = 60.95 t. for 100% efficiency Wi-Py = 500h Wy=275000 e6ttls WT - Wr - 275000 is ng 180 62-88100 W1 = 43.79ft = e, ez les

→ , = 23.79 + 39.06710 0; = 92.85 ft +V? 38 387 – +2 92.85 = l + 20 to 62.8 - P = 5438.48 Lb/ft? (P = 37.76 esi