# A centrifugal pump delivers 1000 litres per minute at 2000 RPM against total head of 50 mts, and requires 32 BHP for its operation. If speed is reduce

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A centrifugal pump delivers 1000 litres per minute at 2000 RPM against total head of 50 mts, and requires 32 BHP for its operation. If speed is reduced to 1000 RPM, the discharge and head developed will be
1. 500 l/min and 25 mtr
2. 500 l/min and 12.5 mtr
3. 250 l/min and 12.5 mtr
4. 250 l/min and 25 mtr

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Correct Answer - Option 2 : 500 l/min and 12.5 mtr

Concept:

For pump:

$\frac{\sqrt H_1}{D_1N_1} = \frac{\sqrt H_2}{D_2N_2}$ ...(i)

$\frac{Q_1}{D_1^3N_1} = \frac{Q_2}{D_2^3N_2}$ ...(ii)

Where, H = Head, D = Diameter, N = Speed, Q = Discharge

Calculation:

Given:

H1 = 50 m, Q = 1000 l/min, N1 = 2000 RPM, N2 = 1000 RPM

Using equation (i)

$\frac{\sqrt H_1}{D_1N_1} = \frac{\sqrt H_2}{D_2N_2}$

$\frac{\sqrt 50}{2000} = \frac{\sqrt H_2}{1000}$

H2 = 12.5 m

Now, using (ii)

$\frac{Q_1}{D_1^3N_1} = \frac{Q_2}{D_2^3N_2}$

$\frac{1000}{2000} = \frac{Q_2}{1000}$

Q2 = 500 l/min.