Question

Water (density 998 kg/mº, dynamic viscosity 0.001 Pa s) is pumped between two reservoirs at a volumetric flow rate of 0.006 m/s through a 120-m long pipe of 5 cm diameter. The roughness ratio of the pipe is a/d = 0.001. There are some fittings and valves in the pipe system, as shown in Figure Q1. The loss coefficients of the valves and fittings can be found in Table Q1. The Darcy friction factor can be found in the Moody chart at the end of the exam paper. (a) Calculate the total minor head loss of water in the system between the two reservoirs [3] (b) Calculate the head loss of water due to pipe friction in the system between the two reservoirs [3] Now the pump is replaced by a turbine and water flows from reservoir to reservoir as driven by the gravity. Assume all other parameters of the system are unchanged. There can now be energy conversion from the flowing water to the rotor of the turbine. (c) Present the Bernoulli equation that applies to the water flow in this system. [7] (d) Calculate the power can be extracted from the turbine (in units of Watts). [7] 2 = 40 m Screwed regular 90* elbow Sharp exit 21 6 m Sharp entrance Half-open gate valve 0.3 m bend radius Pump 120 m of pipe, d = 5 cm Open globe valve Figure Q1 Table Q1 Loss coefficient 0.5 6.9 Fittings and valves Sharp entrance Open globe valve 0.3 m radius bend Regular 90° elbow Half-open gate valve Sharp exit 0.25 0.95 3.8 1.0

Answer 1

= 998 199/m3 Re = PVD M M 0.00! Pad. Ed=0.001 D: 0.05 m Q = 0.006 m/ Lardom A = 0 = 1.963 X602 m 2 Q = VA Y = 3.051m/s (velocity 0.006 1.963x10 fow). of Reynolds nummber 20W/ the = BUD 998 x 3.056x 0.05 u (turbulent flow). Re = 152494 2, -40 2,-60 mino's losses Sharp Entrance = k uz » hran 29. = 0.5% 3.056 = 0.238m. 2x9.71 open globe Valve a hion = 6.9 x 0.476 0.3m radius bend a hion = 29. 90° Elbow - hion = 3.8 XVI • Sharp Ents) how= 2 19 29 CS Scanned with CamScanner . 0.25 X V2 . 0.95 12 gak value

(9) Totul minor los he = 6.5+ 6.9+0.25 +0.95 + 3.8+1, 1) 13.4 x 3.056² 2x9.1 6. 3784 m. (6) chead lon due to friction (major loss). flv² Hin 29. f = fretion fontor { from moedy oliegum? moody chart. Relative pipe soughness - 0.0 0.00 he = 15 2494 0.00|----- fb.co f = 0.023 2 Home - 0.023 X lo x 3.056 2 x 9.81 X 0.05 26.275 m. How = 26.275 m (C) Bernoulli squation between 0 and 0. Pi + PV, ² + 8gh, & pp = P2 + 1 8 V² + 5ghz + 891 sg (hout hug) 2 Head lon 218 + 4x + + + + الی 39 pg 29 Per pump power P = P2 = Palma ,-6m). V = Vzom hz=4om CS Scanned with CamScanner

Polrwyt ti + Head loss totul وعمر ومر ( When thon). hi + (Power ) = he + 4) + (Herthian). 60-6) + (26. + 6.38 - Power. = 66.655 m the power required for the to flow the water 0.006%%. pump Power = 66.655 m of head (Somer in terms of head). power from turbine, 89Q AHM 40-c) - 26-27 651) het head sh = 1.345 m. Perline = 89 Q AHM Y = Efficiemy | Canuming = 999x9.87X0.006*1.345X0.8 80% Efficient 63.21 w CS Scanned with CamScanner