Question

A well located at 750 feet above sea level has a below ground surface water depth of 38 \(\mathrm{ft}\) and pumps to a water tank at an elevation of \(1,030 \mathrm{ft}\) above sea level. The water main from the well to the tank has a total head loss of 11 psi. What is the TH in feet?

Short answer

TH is 305.41 feet.

Step-by-step solution

- Determine the Elevation Gained

Calculate the elevation gain from the well to the tank. The tank is at 1030 feet above sea level, and the well is at 750 feet. The elevation gained is: 1030 - 750 = 280 feet.

- Convert Head Loss from psi to Feet

Use the conversion formula to convert head loss from psi to feet. The formula is: 1 psi = 2.31 feet of head.Given head loss is 11 psi, so: 11 psi * 2.31 = 25.41 feet.

- Determine the Total Head (TH)

Sum the elevation gain and the head loss (converted to feet). TH = 280 feet + 25.41 feet TH = 305.41 feet.

Key concepts

Elevation Gain

To determine the elevation gain in a water pumping system, start by identifying the height difference between the source and the destination. In our example, the water is pumped from a well located at 750 feet above sea level to a tank at 1030 feet above sea level. To calculate the elevation gain:

The difference between these two elevations is:
1030 feet - 750 feet = 280 feet.

So, the elevation gain in this system is 280 feet. This is a crucial aspect because it represents the height the water needs to be pumped, and it's important in calculating the total head required for the system.

Head Loss Conversion

Next, let's discuss how to convert head loss from psi (pounds per square inch) to feet. Head loss occurs due to friction and other factors as water travels through the pipes. It's essential to convert this head loss to the same unit as elevation gain (feet), to sum them accurately.

The conversion factor between psi and feet is 1 psi = 2.31 feet of head. In the example provided, the head loss is 11 psi.
To find the head loss in feet, we multiply the psi by the conversion factor:
11 psi * 2.31 feet/psi = 25.41 feet.

Converting head loss into feet helps us to combine it with the elevation gain to get the total head required for the system.

Water Pumping System

In a water pumping system, the total head (TH) is a critical parameter. It combines the elevation gain and the head loss due to friction and other factors. Let's piece everything together.

From the previous calculations:

• Elevation Gain = 280 feet
• Head Loss = 25.41 feet

Total Head (TH) is the sum of these two values:
TH = Elevation Gain + Head Loss Conversion.
Therefore, TH = 280 feet + 25.41 feet = 305.41 feet.

This total head represents the energy needed by the pump to lift water from the well to the tank, considering both the elevation difference and the head loss due to the water moving through the system.

Understanding the total head is essential for designing and selecting the appropriate pump for an efficient water pumping system.