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: Determine 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 \(P\) represents 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 all 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: Compute the power in Watts.
\[P = 1000 \times 9.81 \times 0.01 \times 38 = 3727.8 \text{ Watts}\] Step 4: Convert the 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. The options provided (1.5, 10, 19, 22) are incorrect, indicating a potential error in the original question or its options. The calculated result is 5.0 HP.