At 1800 rpm, a centrifugal pump discharges 50 L/s at its best-efficiency point for a total head of 25 m. Find the specific speed of the pump (rpm). (Rounded to 2 decimal places)
Official Answer Key:
35.90 to 36.10
Step-by-Step Solution & Explanation
• **Governing Equation (Specific Speed of Centrifugal Pump):**
$N_s = \frac{N \sqrt{Q}}{H^{3/4}}$
• **Given Data:**
- Rotational speed $N = 1800\text{ rpm}$.
- Discharge $Q = 50\text{ L/s} = 0.05\text{ m}^3/\text{s}$.
- Total dynamic head $H = 25\text{ m}$.
• **Calculation:**
- $\sqrt{Q} = \sqrt{0.05} = 0.223607$.
- $H^{3/4} = 25^{0.75} = (25^{1/4})^3 = (2.236068)^3 = 11.18034$.
$N_s = \frac{1800 \times 0.223607}{11.18034} = \frac{402.492}{11.18034} = 36.00\text{ rpm}$
• **Conclusion:** The specific speed of the pump is $36.00$ (Official range: 35.90 to 36.10).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.