Question 9.CSGP.135: A pump receives water at 100 kPa, 15°C and a power input of ......

Fundamentals of Thermodynamics – Solution Manual [1477300]

A pump receives water at 100 kPa, 15°C and a power input of 1.5 kW. The pump has an isentropic efficiency of 75% and it should flow 1.2 kg/s delivered at 30 m/s exit velocity. How high an exit pressure can the pump produce?

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CV Pump. We will assume the ideal and actual pumps have same exit pressure, then we can analyse the ideal pump.
Specific work: $w _{ ac }=1.5 / 1.2=1.25 \,kJ / kg$

Ideal work Eq.9.27: $w _{ s }=\eta w _{ ac }=0.75 \times 1.25=0.9375 \,kJ / kg$

As the water is incompressible (liquid) we get
Energy Eq.9.14:

\begin{aligned}w _{ s } & =\left( P _{ e }- P _{ i }\right) v + \mathbf{V} _{ e }^2 / 2=\left( P _{ e }- P _{ i }\right) 0.001001+\left(30^2 / 2\right) / 1000 \\& =\left( P _{ e }- P _{ i }\right) 0.001001+0.45\end{aligned}

Solve for the pressure difference

\begin{aligned}& P_e-P_i=\left(w_s-0.45\right) / 0.001001=487 \,kPa \\& P_e= 5 8 7 \,k P a\end{aligned}

Water pump from a car

102

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