Respuesta :
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
[tex]{W_{u}}= \eta {W_{pump}}[/tex] .............1
put here value
[tex]{W_{u}}[/tex] = (0.80)(20)
[tex]{W_{u}}[/tex] = 16 hp
and
now we get change in the total mechanical energy of water is equal to the change in its potential energy
[tex]\Delta{E_{mech}} = {m} \Delta pe[/tex] ..............2
[tex]\Delta {E_{mech}} = {m} g \Delta z[/tex]
and that can be express as
[tex]\Delta {E_{mech}} = \rho Q g \Delta z[/tex] ..................3
so
[tex]\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}][/tex] ......4
solve it we get
[tex]\Delta {E_{mech}} = 13.614[/tex] hp
so here
due to frictional effects, mechanical power lost in piping
we get here
[tex]{W_{frict}} = {W_{u}}-\Delta {E_{mech}}[/tex]
put here value
[tex]{W_{frict}}[/tex] = 16 -13.614
[tex]{W_{frict}}[/tex] = 2.37 hp
so mechanical power used to overcome frictional effects in piping is 2.37 hp
