Discussion
A centrifugal pump running at 500 rpm and at its maximum efficiency is delivering a head of 30 m at a flow of 60 liters per minute. If the rpm is changed to 1000, then the head H in meters and flow rate Q in liters per minute at maximum efficiency are estimated to be :
Answer: C
At 1000 rpm the pump gives H = 120 m and Q = 120 litres per minute.
For the same pump running at its point of maximum efficiency, the affinity laws say that discharge varies as the speed and head as the square of the speed.
\[ \begin{aligned} \frac{Q_2}{Q_1} &= \frac{N_2}{N_1} = \frac{1000}{500} = 2 \\ Q_2 &= 2 \times 60 = 120\ \text{L/min} \end{aligned} \]
\[ \begin{aligned} \frac{H_2}{H_1} &= \left(\frac{N_2}{N_1}\right)^{2} = 4 \\ H_2 &= 4 \times 30 = 120\ \text{m} \end{aligned} \]
H = 60 m comes from scaling the head linearly with speed, Q = 30 halves the flow instead of doubling it, and Q = 480 cubes the speed ratio, which is the law for power, not for flow.
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