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.

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