A centrifugal pump is to be placed over a large open water tank and is to pump water at a rate of 3.5 x 10^(-3) m^3/s. At this flow rate, the value of NPSH given by the manufacturer is 4.5 m. If the water temperature is 15°C and atmospheric pressure .of 10 kPa, determine the maximum height that the

Question

A centrifugal pump is to be placed over a large open water tank and is to pump water at a rate of [latex]3.5 x 10^{-3 } m^{3}/s[/latex]. At this flow rate, the value of NPSH given by the manufacturer is 4.5 m. If the water temperature is 15°C and atmospheric pressure .of 10 kPa, determine the maximum height that the pump can be located above the water surface without cavitation. Assume the major head loss between tank and the pump is due to filter at the pipe inlet having a minor loss coefficient of 20. Other losses being neglected, the pipe on the suction side of the pump has a diameter of 10 cm.

Accepted Answer

Given [latex]Q = 3.5 imes 10^{-3} m^{3}/s ; NPSH = 4.5 m t = 15° C P_{atm} = 101 kPa, k = 20[/latex]

NPSH is given by the equation NPSH =[latex]\frac{P_{atm}}{\gamma}- z_{1} -\sum{ h_{1}} - \frac{P_{v}}{\gamma}[/latex]

[latex]z_{1} = \frac{P_{atm}}{\gamma} - \sum{ h_{1}} - \frac{P_{v}}{\gamma} -NPSH[/latex]

Velocity in the suction pipe [latex]V = \frac{Q}{A}=\frac{3.5 imes 10^{-3}}{\frac{\pi}{4} imes 0.1^{2}}=0.45[/latex]m/s

[latex]\sum{ h_{1}}=k\frac{V^{2}}{2g}=\frac{20 imes0.45^{2}}{2 imes 9.8}=0.2[/latex]

Vapour pressure [latex]P _{v} [/latex] at 15°C = 1666 Pa

substituting proper values,
[latex] z_{1} = \frac{101 imes 10^{3}}{ 9800 }-0.2-\frac{1666}{9800}-4.5=10.3-0.2-0.17-4.5=5.43[/latex]m

The pump should be located higher than 5.43 m above the water surface.

Question 8.7: A centrifugal pump is to be placed over a large open water t...

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