Question 7.230E: Redo Problem 7.198E if the water pump has an isentropic effi...

C.V.: pump + hose + water column, total height difference 110 ft. Here V is velocity, not volume.

Continuity Eq.4.3, 4.11:          \dot{ m }_{ in }=\dot{ m }_{ ex }=(\rho A V )_{ nozzle }

Energy Eq.4.12:                        \dot{ m }\left(- w _{ p }\right)+\dot{ m }\left( h + V ^{2} / 2+ g z\right)_{ in }=\dot{ m }\left( h + V ^{2} / 2+ g z\right)_{ ex }

Process:

Recall the conversion  1  Btu / lbm =25037   ft ^{2} / s ^{2} from Table A.1. The velocity in the exit nozzle is such that it can rise 30 ft. Make that column a C.V. for which Bernoulli Eq.7.17 is:

Assume:        v = v _{ F , 70 F }=0.01605   ft ^{3} / lbm

……………………………

Eq.4.3 : \dot{m}=\rho_{ avg } \dot{V}=\dot{V} / v=\int\left( V _{\text {local }} / v\right) d A= V A / v

Eq.4.11 : \dot{m}_{i}=\dot{m}_{e}=\dot{m}

Eq.4.12 : \dot{Q}_{ C.V .}+\dot{m}\left(h_{i}+\frac{ V _{i}^{2}}{2}+g Z_{i}\right)=\dot{m}\left(h_{e}+\frac{ V _{e}^{2}}{2}+g Z_{e}\right)+\dot{W}_{ C . V. }

Eq.7.17 : v P_{i}+\frac{1}{2} V _{i}^{2}+g Z_{i}=v P_{e}+\frac{1}{2} V _{e}^{2}+g Z_{e}