Question

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.

Answer 1

10.386hp

Step-by-step 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