Question

If a water pump delivers 10 liters of water in one second against the head of 38 meters, the water horse power required will be:

• A. 5.0
• B. 10
• C. 19
• D. 22

Hint:

A useful shortcut for calculating Water Horsepower is: \[ \text{WHP} = \frac{Q (\text{L/s}) \times H (\text{m})}{75} \] Using this: \( \text{WHP} = \frac{10 \times 38}{75} = \frac{380}{75} \approx 5.07 \) HP. Always be cautious of units and potential errors in question data. The power calculated here is the water horsepower; the required brake horsepower of the motor would be higher due to pump inefficiency.

Answer 1

The Correct Option is A

Step 1: Identify the formula for Water Horse Power (WHP).
The power imparted to the water by the pump is calculated as: \[ P = \rho \cdot g \cdot Q \cdot H \] where \(P\) is power in Watts, \( \rho \) is the density of water (\(\approx 1000\) kg/m\(^3\)), \(g\) is the acceleration due to gravity (\(\approx 9.81\) m/s\(^2\)), \(Q\) is the flow rate in m\(^3\)/s, and \(H\) is the total head in meters.
Step 2: Convert the given values to SI units.
- Flow Rate, \(Q = 10\) liters/second \( = \frac{10}{1000} \) m\(^3\)/s \( = 0.01 \) m\(^3\)/s
- Head, \(H = 38\) m
- Density, \(\rho = 1000\) kg/m\(^3\)
- Gravity, \(g = 9.81\) m/s\(^2\)
Step 3: Calculate the power in Watts. \[ P = 1000 \times 9.81 \times 0.01 \times 38 = 3727.8 \text{ Watts} \] Step 4: Convert power from Watts to Horsepower (HP).
The conversion factor is 1 HP \(\approx 746\) Watts. \[ \text{WHP} = \frac{3727.8 \text{ W}}{746 \text{ W/HP}} \approx 4.997 \text{ HP} \approx 5.0 \text{ HP} \] The calculated Water Horsepower is approximately 5.0 HP. None of the options (1.5, 10, 19, 22) provided in the original question are correct. There is likely an error in the question or options. Based on calculation, the answer is 5.0.