Question

Problem 4 (10 points) A pipeline with two pumps (Pump A and Pump B) in series delivers water between two tanks with a total static head of 50 ft. The pipeline is 8 inches in diameter and 5000 ft in length, with a Darcy- Weisbach friction factor f = 0.025. The total minor head loss coefficient Ek 20. The characteristics of the two pumps are shown in the following table. Determine (a) the operating conditions of head and discharge, (b) head developed by each pump, and (c) input power. Capacity-Head-Efficiency Relations for Pump A and Pump B Pump B Q (cfs) Pump A Efficiency (%) H (ft) H (ft) Efficiency (%) 0.00 124 0 144 0 1.11 119 54 139 57 1.78 112 65 132 67 2.23 104 68 124 70 2.90 90 70 110 72 3.56 70 67 90 69

Answer 1

- - V: 0 A Given desin = 0.666 ft L=5000 ft flv2 Major Head loss, hf 290 2.864 0 ft/s Ix0,6602 4 hf - 0.025 x 5000x (2.8640)? 23.8802 2x 32.2 x 0.666 Minor head loss, hminor & KLU? 20 (2.864922 2.547 02 29 . 2x322 Required Head .. Hpump = Hstatic + hmajur + hminor H = 50 + 23.880 +2.54702 | #250 +26427021 Hsystem veq Head developed by pumps in series, H= Hit H₂ = HATHB Hrequired ft) a (ft²) Hpumpe Hat HB (44) 50 268 82.56 258 1.78 133.73 244 2.23 181.41 228 2.90 272.25 200 3.56 384.92 160 The operating point lies between Q = 2.23 to 290 cfs At 0-2.5 ft/s - Hrequired (2.5-2.23) Hpump = 228 (Interpolation) 216 ft = 215 ft (228-200) (2.90-2,23) x

(a) Operating point Of Pump : Q=2.5 fts, H=216 ft (b) Head developed by each pump: HA = 104 98.35 ft (104-90) (2.5-2,23) (29-2.23) (124-110) (2.5-2,43) (2.9-223) HB: 124 118.35 ft (C) At Q=2.5 ft/s, NA = 69%. No=71% Input power, P: Pg O HA + SQQ HB NA no

Р= "ФНА t 11 В ФHB NA 6,4 хе. 5x98. 35 + 0,69 62.4 xа. 5x /18.35 О) 48& 39, 319 lbf- к ft 817 hp