Question

What is the required water horsepower for 100 gpm and a total head pressure of \(50 \mathrm{ft}\) ?

Short answer

The required water horsepower is approximately 1.26 HP.

Step-by-step solution

- Understand the Required Formula

The formula to calculate the water horsepower (WHP) is: \[ WHP = \frac{{Flow \times Head}}{{3960}} \]where Flow is in gallons per minute (gpm) and Head is in feet (ft).

- Substitute Given Values into the Formula

Given Flow = 100 gpm and Head = 50 ft, substitute these values into the formula: \[ WHP = \frac{{100 \times 50}}{{3960}} \]

- Calculate the Water Horsepower

Perform the calculation: \[ WHP = \frac{{5000}}{{3960}} \approx 1.26 \text{{ horsepower}} \]

Key concepts

Water Flow Rate

Water flow rate refers to the volume of water that passes a particular point within a specified time.
This is usually measured in gallons per minute (gpm). Understanding water flow rate is fundamental when dealing with hydraulic systems, as it impacts efficiency and performance.

Flow rate helps determine the power needed in systems such as irrigation or water supply. For instance, in our exercise, the water flow rate is given as 100 gpm.
This means that 100 gallons of water move through the system every minute.

Flow rates can vary based on system design and requirements, and knowing the flow rate is crucial to calculate horsepower accurately.

Total Head Pressure

Total head pressure measures the height that a pump can lift water, often represented in feet (ft).
This concept combines several types of pressure: atmospheric, elevation, and system pressure.
In simpler terms, total head pressure accounts for the overall effort needed to move water to the required height and through the system.

In our exercise, the total head pressure is given as 50 ft. This means the pump needs to lift or push water up to 50 feet high. Calculating total head pressure ensures you select the right pump for your needs, preventing inefficient operation or system failures.
Properly accounting for total head pressure is essential for accurate water horsepower calculations.

Horsepower Formula

Horsepower is a unit of measurement that indicates the power of the pump needed to move water. To find the water horsepower (WHP), use this formula:
\[ WHP = \frac{{Flow \times Head}}{{3960}} \]
The formula requires the flow rate (in gpm) and the total head pressure (in feet).

In the provided exercise, the flow rate is 100 gpm, and the head pressure is 50 ft.
Substitute these values into our formula: \[ WHP = \frac{{100 \times 50}}{{3960}} \]
When you calculate it, you get approximately 1.26 horsepower.
This calculation is important because it tells you how powerful your pump needs to be to effectively move the water through the system.