Water is pumped from a reservoir to a height of 1000 m from the reservoir level, through a pipe of 15 cm I.D. at an average velocity of 4 m/s. If the pipeline along with the fittings is equivalent to 2000 m long and the overall efficiency is 70%, what is the energy required for pumping? Friction factor f = 0.046 Re-0.2.
Data:
Diameter of pipe (D) = 15 cm
Average Velocity (v) = 4 m/s
Equivalent Length of pipe with fittings = 2000 m
Efficiency of pump (η) = 0.7
Formula:
Calculations:
Re = Dvρ/μ
= 0.15 x 4 x 1000/0.001 = 600000
f = 0.046 x (600000)-0.2 = 0.003215
hf = 2 x 0.003215 x 2000 x 42/0.15 = 1371.73 m2/sec2
Frictional losses per unit weight (h)= hf/g = 1371.73/9.812 = 139.8 m
Power required for pumping = mass flow rate x g x h / efficiency of pump
Mass flow rate = volumetric flow rate x density
= velocity x cross sectional area x density
= 4 x (πD2/4) x ρ
= π x 0.152 x 1000 = 70.686 kg/sec
power required = 70.686 x 9.812 x 139.8/0.7 = 96961 watt = 138515.7 watt = 138.5 KW
Last Modified on: 04-Feb-2022
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