Calculating the flow pumped through a pipe

Applying equation (4.81) to the pipe connecting the suction vessel to the pump, the mass flow is given by  

Similarly, the flow from the pump exit to the discharge vessel is given by  

Here the specific volume, V, has been retained because the temperature rise across the pump is usually small. Squaring and adding the last two equations produces  

Equation (17.50) implies that, as far as the calculation of flow is concerned, it does not matter where the pump is situated in the line between the suction and discharge vessels. [Note that it does mattter in practice, and the pump will normally be situated as near the suction vessel as possible, so as to avoid the pump s inlet pressure falling below the vapour pressure of the liquid, when cavitation will reduce pumping efficiency and cause damage to the pump.] 

The head developed across the pump at speed, N, is given by equation (17.28), and the corresponding pressure difference is  

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