Question

7) (7 marks) Water (p = 1000 kg/m?, v = 1 x 10-6 m²/s) for an irrigation system is to be pumped through a pipe from a reservoir to crop fields that are a distance along the ground of 1.1 km from the reservoir. The fields are at an elevation that is 20 m above the reservoir. The diameter of the pipe is 0.2 m. The required volume flow rate is 0.2 m/s. The steel pipe has an average roughness of 0.04 mm. The pipe is to be fitted with a single globe valve that has a loss coefficient of K =1.5. Determine the power required to drive the pump if the pump efficiency is assumed to be 75%.

Answer 1

0.2 m²lone :2=1.1 km =) lloom d = 0.2 032 6366 in Isec А (0.232 Re - VD 6.366.80:02 (Reylonds 9 lx.106 number) 127.3239.5 & € absoulute roughness) 0.04 x lom & (relative roughness) 0.04.x10} (ح 0.2 Chio) hi 2 - e) 2x10 him from Moody's chart friction factor (FD = Duolys so major losses Fli? zdg. 0.0145 x (1 100) x 6.366 2x0.2 x 9.8) 164:72 . minor losses z hlze Ek v² 29 Eky ik tk. valve D.S +1 +1:5 Ek = a 2 M2I= exit 22

hl= giever है Teg. - 2x. 63602 2x908) h z = 4.13 m Total head loss os hizhithiz - 164.72 +4.13 Total head loss Chl) 2) 168.85 m Now apply Bernoull's therom. at Jieser voir and field ity + Kithe P/ +4² + Z, the 29 Pi= P2 = Patm Vi=0 (roservior) V2= 6.366, Z2. Zom hiz 168-85 m he= 6.3662 t 20+ 168.85 29 hp=. 190.91 m pumping Power = P Q glip 2) 1000 x 0.2% 9.81 x 190.91 Pumping Power & 374.5 65.42 w Power required Power n. z) 374.56514 0.75 o 499420.56.W or 27 1999.4 kw)