Question

An 80-percent-efficient pump with a power input of 20 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

Answer:

mechanical power used to overcome frictional effects in piping is 2.37 hp

Explanation:

given data

efficient pump = 80%

power input = 20 hp

rate = 1.5 ft³/s

free surface = 80 ft

solution

we use mechanical pumping power delivered to water is

${W_{u}}= \eta {W_{pump}}$  .............1

put here value

${W_{u}}$  = (0.80)(20)

${W_{u}}$ = 16 hp

and

now we get change in the total mechanical energy of water is equal to the change in its potential energy

$\Delta{E_{mech}} = {m} \Delta pe$   ..............2

$\Delta {E_{mech}} = {m} g \Delta z$  

and that can be express as

$\Delta {E_{mech}} = \rho Q g \Delta z$     ..................3

so

$\Delta {E_{mech}} = (62.4lbm/ft^3)(1.5ft^3/s)(32.2ft/s^2)(80ft)[\frac{1lbf}{32.2lbm\cdot ft/s^2}][\frac{1hp}{550lbf \cdot ft/s}]$      ......4

solve it we get

$\Delta {E_{mech}} = 13.614$ hp

so here

due to frictional effects, mechanical power lost in piping

we get here

${W_{frict}} = {W_{u}}-\Delta {E_{mech}}$  

put here value

${W_{frict}}$ = 16 -13.614

${W_{frict}}$ = 2.37  hp

so mechanical power used to overcome frictional effects in piping is 2.37 hp