Question

An agricultural pump lifts water from a well with a discharge of 1,00,000 liters/hour against a head of 20 m. What is the water power in watts?

• A. 5.4936
• B. 54.936
• C. 549.36
• D. 5493.6

Hint:

Convert discharge to m³/s and use \( P = \rho g Q H \) to calculate water power.

Answer 1

The Correct Option is D

Step 1: Water Power Formula
Water power (\( P \)) is given by: \[ P = \frac{\rho g Q H}{3600} \] where: - \( \rho \) = Density of water (1000 kg/m³) - \( g \) = Acceleration due to gravity (9.81 m/s²) - \( Q \) = Discharge in m³/s - \( H \) = Head in meters
Step 2: Converting Given Data
\[ Q = \frac{100000}{3600} = 27.78 \text{ l/s} = 0.02778 \text{ m³/s} \]
Step 3: Substituting Values
\[ P = 1000 \times 9.81 \times 0.02778 \times 20 \] \[ P = 5493.6 \text{ W} \]