# A water pump increases the water pressure from 15 psia to 70 psia. Determine the

A water pump increases the water pressure from 15 psia to 70 psia. Determine the power input required, in hp, to pump 0.8 ft^3/s of water. Does the water temperature at the inlet have any significant effect on the required flow power? Answer: 11.5 hp
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Cleveland Walters
Given:
${p}_{1}=15\psi a$
${p}_{2}=70\psi a$
${\stackrel{˙}{V}}_{ol}=0.8f\frac{{t}^{3}}{s}$
Solution:
Note: $\stackrel{˙}{m}=\rho ×{\stackrel{˙}{V}}_{ol-}\left(as\sum \in g\in co\mp ressib\le flow⇒\rho =const\right)$
The total change in the system mechanical energy can be calculated as follows,
$\mathrm{△}e=\frac{{p}_{2}-{p}_{1}}{\rho }$
The power needed can be calculated as follows,
$P=\stackrel{˙}{W}=\stackrel{˙}{m}\mathrm{△}=\rho ×{\stackrel{˙}{V}}_{ol}×\frac{{p}_{2}-{p}_{1}}{\rho }={\stackrel{˙}{V}}_{ol}×\left({p}_{2}-{p}_{1}\right)$
$=44\left(\psi a\cdot f\frac{{t}^{3}}{s}\right)=44\left(\psi a\cdot f\frac{{t}^{3}}{s}\right)×\left(\frac{1Btu}{5.404\psi a\cdot f{t}^{3}}\right)\left(×\frac{1hp}{0.7068Bt\frac{u}{s}}\right)=11.52hp$
Finally answer: $P=11.52hp$