A six-stage centrifugal pump delivers 150 L/s at a net pressure rise of 5003 kN/m², impeller speed 1450 rpm, g = 9.81 m/s². Find the specific speed. (Answer in integer)
Official Answer Key:
631 to 637
Step-by-Step Solution & Explanation
• **Concept & Given Data:**
- Multistage pump delivering high head: number of stages $n = 6$.
- Net pressure rise $\Delta P = 5003\text{ kN/m}^2 = 5,003,000\text{ N/m}^2$.
- Density of water $\rho = 1000\text{ kg/m}^3$, acceleration due to gravity $g = 9.81\text{ m/s}^2$.
- Total dynamic head $H_{total} = \frac{\Delta P}{\rho g} = \frac{5,003,000}{1000 \times 9.81} = 510.0\text{ m}$.
- Head per stage $H_{stage} = \frac{H_{total}}{n} = \frac{510.0}{6} = 85.0\text{ m}$.
• **Specific Speed per Impeller Stage:**
- In standard Indian pump engineering practice with $Q$ in $\text{L/s}$ and $H$ in $\text{m}$:
$N_s = \frac{N \sqrt{Q}}{H_{stage}^{3/4}} = \frac{1450 \times \sqrt{150}}{85^{3/4}}$
- $\sqrt{150} = 12.2474$
- $85^{3/4} = (85)^{0.75} = 27.9745$
$N_s = \frac{1450 \times 12.2474}{27.9745} = \frac{17758.7}{27.9745} = 634.82 \approx 635$
• **Conclusion:** Specific speed is $635$ (Official range: 631 to 637).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.