Determine the Horsepower Required to Pump Water 100 Feet in Elevation Using a 4-Inch Line

When it comes to pumping water to a height of 100 feet through a 4-inch line, selecting the appropriate horsepower is crucial for efficient and effective operation. This article aims to guide you through the process of calculating the required horsepower, including the importance of flow rate, head, and water weight.

Understanding the Formula and Variables

To accurately determine the horsepower needed for your water pumping task, you can use the following formula:

Horsepower (HP) (Flow Rate (GPM) × Head (ft) × Water Weight (lb/ft3)) / 3960

Variables Explanation

Flow Rate (GPM): This is the gallons per minute you wish to pump. Head (ft): This is the vertical distance the water is lifted, which in this case is 100 feet. Water Weight (lb/ft3): The density of water is approximately 62.4 pounds per cubic foot.

Calculation Steps

Let's walk through the calculation process with an example. Suppose you want to pump 100 gallons per minute (GPM) of water 100 feet in elevation.

Step 1: Convert Flow Rate to Cubic Feet per Minute (CFM)

First, convert the flow rate from gallons per minute to cubic feet per minute:

Flow Rate (CFM) Flow Rate (GPM) × 0.133681

For a 100 GPM flow rate:

100 GPM × 0.133681 ≈ 13.3681 CFM

Step 2: Calculate the Horsepower

Now, plug the values into the formula to calculate the horsepower:

HP (100 × 100 × 62.4) / 3960

HP 624000 / 3960 ≈ 157.58 HP

Time Considerations and Real-World Applications

It's essential to consider the time it takes to achieve the desired flow. Using the example above, if you aim to pump 100 GPM at 157.58 HP, it would indeed take a long time. In practical scenarios, such as moving water for irrigation over a period of hours, actual horsepower requirements can be significantly lower due to the extended operation time.

Example Calculation with Time Factor

If you have 1/10 HP available, it might take a full day to fill a 4-inch pipe to 100 feet elevation. Here’s how to factor in time:

To fill the pipe, you would need:

Hydraulic Power Work / Time

Work done in moving the water can be estimated using:

Work Volume × Height × Specific Gravity

For simplicity, we’ll use an example where you need to provide 35 cubic meters per hour through a vertical 4-inch PVC line:

Step 1: Calculate Friction Losses

The pressure loss due to friction in vertical PVC pipes is typically calculated as:

Pressure loss per 100m 1.3m

For 100 feet (30.48m), the pressure loss will be:

Pressure loss 30.48m × 1.3 / 328.08m ≈ 0.39624m

Step 2: Calculate Required Power

The power required is given by:

Power (Density × Volume flow rate × Gravity × Height) / 1000

Assuming water density (ρ) ≈ 1000 kg/m3, 35 cubic meters per hour (Q), gravity (g) ≈ 9.81 m/s2, and height (h) 0.39624m:

Power (1000 × 35/3600 × 9.81 × 0.39624) / 1000 ≈ 2944.82 Watts

Power ≈ 3.92 HP

Conclusion

To pump water 100 feet in elevation using a 4-inch line, you need to calculate the required horsepower based on your specific flow rate and time constraints. In general, a 100 GPM flow rate would require approximately 157.58 HP, while a 1/10 HP system might take a full day to achieve the same task. Understanding and correctly applying the formula and variables are crucial for efficient water pumping operations.

Keywords: horsepower for water pumping, pump water elevation, water pressure calculation