GATE 2025 AG – Question 45
A six-stage centrifugal pump delivers 150 L/s against a net pressure rise of 5003 kN/m² at 1450 rpm. Use $g=9.81\,\mathrm{m/s^2}$. Find pump specific speed as an integer.
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Correct answer: 631 to 637
Explanation
Total water head is $H=\Delta p/(\rho g)=5003000/(1000\cdot9.81)=510.0$ m. Each of six identical stages develops 85.0 m. The conventional litre-per-second specific-speed index is $N_s=N\sqrt{Q}/H_{stage}^{3/4}=1450\sqrt{150}/85^{3/4}=634.39$,rounded **634**. The numerical index depends on the stated Q convention; using m³/s would give 20.06 rather than the official L/s index.