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.