If a pump is pumping at 15KW, what is the water horsepower for a 15HP pump?

To calculate the water horsepower (WHP) for a pump, we need to understand that the formula for water horsepower (WHP) is:

\[
WHP = \frac{{Q \times H}}{{3960}}
\]

Where:
- \( Q \) is the flow rate in gallons per minute (GPM),
- \( H \) is the head in feet,
- 3960 is a constant for converting between horsepower, flow rate, and head.

However, you are asking about a 15 HP pump, and if the pump is operating at 15 kW, we first need to convert the electrical power (in kW) to mechanical horsepower (HP), and then calculate the water horsepower based on the efficiency of the pump.

### Steps:
1. **Convert electrical power (kW) to mechanical horsepower (HP)**:
   \[
   1 \, \text{kW} = 1.341 \, \text{HP}
   \]
   So, the mechanical horsepower of a 15 kW pump is:
   \[
   \text{Mechanical HP} = 15 \, \text{kW} \times 1.341 = 20.115 \, \text{HP}
   \]

2. **Determine water horsepower**: The actual water horsepower (WHP) is the useful power delivered to the water, and it depends on the pump efficiency (\( \eta \)):

   \[
   WHP = \text{Mechanical HP} \times \eta
   \]

   Assuming the efficiency (\( \eta \)) of the pump is around 70% (a typical value for many pumps):
   \[
   WHP = 20.115 \times 0.70 = 14.08 \, \text{HP}
   \]

Thus, the water horsepower is approximately **14.08 HP** for a pump running at 15 kW, assuming 70% efficiency.

Would you like further clarification on any of the steps?

### Related Questions:
1. How does pump efficiency affect water horsepower?
2. What is the relationship between head, flow rate, and water horsepower?
3. How would you calculate water horsepower if the flow rate and head are known?
4. What is the difference between brake horsepower and water horsepower in a pump system?
5. How can improving pump efficiency reduce energy consumption?

**Tip:** Always check the pump's efficiency to make more accurate WHP calculations.

Learn how to calculate the water horsepower (WHP) for a pump operating at 15KW. This example covers power conversion, pump efficiency, and calculating the WHP. Suitable for students in Grades 11-12 or introductory engineering courses.

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