Question

A turbo pump transfers water from tank 1 to tank to tank 2 as shown in the picture below. The diameter of the piping system is D= 4in and the total length of pipes is L=620 ft. the elevation difference is Z1-Z2= 30ft. Use the chart for KL values.

a) determine the flow rate (Q)

b) power of the pump in HP

Note that you can write out both mass balance equation and energy equation of the head form for the control-volume enclosed by the free surfaces, (1) and (2), of the two tanks. You need to consider all minor head losses through fittings, valves, etc. (see the table given). To estimate the major head loss through the straight pipes, the Haaland equation is required to determine the friction factor f. An iteration process is required to find out the friction factor f and the flow rate O simultaneously. You are required to set up the equations and carry out at least two iteration steps. (2) A B (0 Gate Valve II (closed) (1) Gate Pump Valve I (open) KL 1.3 Fittings and Valves 90° elbow (flanged & long radius) Basket Strainer T-joint (line flow) T-joint (branch flow) Exit Gate valve (fully open) 1.0

Answer 1

solution : Given that The diameter of the Piping syslem 15 D: 4 in 10.1016 m. Total length of pipes is 1 : 690 PL = 188.96 m Elevation difference 21-22 = 30 ft = 9.144 m Applying beenculis equation to tank ' Ę tank 2 Pz + 42 +21 ve - of of 22 the Pi Pg 29 eg 29 where, Presswe head in tank1 - 0 Catmospheric poressure Pi c9 5 P2 . Ni a velocity of water in tank 1 = 0 m/s (steady walo) Paressure head in tank 2 : 0 Catmospheric pressione) Ne velocity of wala in -lanka : o mlis (steady wadesi) Me - Total head loss due to for fölict; on Pipe fittings & values. eg ha=h26 (basket shokinesi) + hle C 909 ellow) + hng Chale value) + hej, (T- Joint (line flow)] + heje (T- joint (branch flow) + hledi Centil-) + hep C folichons V2 hi= kb it kg 29 V2 X v2 Kjl a keax 29 t ke. to - Кі, 29 29 29 29 + flue dx29 know that, forom the prioblem, given that We kibe 1.3, Ke = 0 (nol given), Kg: 0 (not givenl, Aj) = 0 Cnot given), Kję = 0 Cnot given) kex alio

substituce all verlay in equation © (2 0+ 0 + 21-29 Oto Photo & Kb. ve + Kar U2 PLU? + 29 29 29 29 Dx 29 Ż-22 Kh.uz V2 + Ken + PLU? 29 29 12 q.144 - 13 x 2x9.81 Dx 29 f *188.976 x v2 +1. V 2 + 2x9.81 0.1016 X 2x 9.81 179.41 = 1.30? +102 + 1860 fui 179,41 02 ( 2.3 + 1860.4) - © in this problem que have only one equation and two einknown, So can't find the solution..80 we have to considered type flow through Pipe and hence vakee of friction factor $-0.02 - C Laminan water flow through pipe) Substitude of value in eduction © 179,4l = V2 (2.3 p + 1860 (0.02)) 179.41 - 39.5 v2 VE 2.131 mis Q, 'The flow glate thorough Pipe co) Q = AX V. AXV = (0.1016)2 x 2.131 Q : 0.0128 m3/s

b. power of pump in HP 3 P= PgQH pg @ [C21-29) + he] 2 - 1000 x 9.81 * 0.01728x] 9. luut 1.3 X 2.131 2x9.81 + 2.131 it 9x9.81 0.02X188.976 x 2.312 01016 X 2x 9.81 P: 3099.800 walts 3. 09987 Klo p. 3.09987 0.746 P. 4. 1553 HP
please give some positive rating..I have less cf score..thank you so much..