Question

If a centrifugal pump is discharging 450 l/min of water with 5 hp motor having efficiency 80%, then calculate the total head, will be

• A. \(6.7 \mathrm{m}\)
• B. \(40 \mathrm{m}\)
• C. \(67 \mathrm{m}\)
• D. \(4 \mathrm{cm}\)

Hint:

Pump power formula: \(P = \frac{\gamma Q H}{75 \eta}\) (hp).
Or \(P = \frac{\rho g Q H}{\eta}\) (W).
Check units carefully: Q in m³/s, H in m.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The total head developed by a centrifugal pump is obtained from the relationship between hydraulic power, discharge, and pump efficiency.

Step 2: Key Formula:
The pump power relation is \[ P=\frac{\rho gQH}{\eta} \] where \[ P=\text{motor power},\; Q=\text{discharge},\; H=\text{total head},\; \eta=\text{efficiency}. \]

Step 3: Calculation:
Given, \[ Q=450~\text{L/min}=0.0075~\text{m}^3/\text{s} \] \[ P=5~\text{hp}=5\times746=3730~\text{W} \] \[ \eta=80\%=0.8 \] Substituting the values, \[ 3730=\frac{1000\times9.81\times0.0075\times H}{0.8} \] \[ 3730=91.97H \] \[ H=\frac{3730}{91.97}\approx40.6~\text{m} \] The calculated head is approximately 40 m, which corresponds to option (B).

Step 4: Final Answer:
H\approx40~m} Hence, the correct answer is (B) 40 m.
[0.5cm]