An 80-percent-efficient pump with a power input of 30 hp is pumping water from a lake to a nearby pool at a rate of 1.5 ft3/s through a constant-diameter pipe. The free surface of the pool is 80 ft above that of the lake. Determine the mechanical power used to overcome frictional effects in piping.

Question

Engineering

Trystan Fowler

14 August, 17:09

An 80-percent-efficient pump with a power input of 30 hp is pumping water from a lake to a nearby pool at a rate of 1.5 ft3/s through a constant-diameter pipe. The free surface of the pool is 80 ft above that of the lake. Determine the mechanical power used to overcome frictional effects in piping.

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Basil · Answer 1

10.386hp

Explanation:

Efficiency of pump (ηp) = 80%=0.80

Flow rate (Q) = 1.5ft^3/s

Input power, P (in) = 30hp

Height (h) = 80ft

Density of water (ρ) = 62.4lbm/ft^3

Acceleration due to gravity = 32.2ft/s^2

To calculate for mechanical power, W (mechanical):

W (mechanical) = (ηp*P (in)) = (0.80) * (30)

Wmechanical = 24hp

To calculate for total mechanical energy ΔE (mechanical):

ΔE (mechanical) = ρ*Q*g*Δh

= (62.4) * (1.5) * (32.2) * (80) * (1lbm) / (550lbm) * ft/s

=13.614hp

To calculate the power lost due to overcoming friction, W (friction):

W (friction) = W (mechanical) - (ΔE) mechanical

= (24-13.614) hp

=10.386hp

Hence, the solution is 10.386hp