Can a Water System's 5.5 HP Submersible Pump Deliver Water to a Remote Location 400 Meters Away with a 35-Meter Elevation Difference?

Understanding the Scenario

When designing a water distribution system, especially one that involves a significant distance and elevation difference, ensuring that the chosen pump can deliver the water efficiently is critical. In this case, you're interested in whether a 5.5 HP submersible pump can deliver water from a starting point 400 meters away, with a height difference of 35 meters.

Converting Units for Consistency

To properly evaluate the system, it's essential to ensure that all units are consistent. Here, we will use feet and pounds per second (lb/sec) as the units of measurement since 1 HP (horsepower) is equivalent to 550 ft lb/sec.

Conversions

400 meters 1,312 feet 35 meters 114.8 feet 2 inches 0.166 feet 2 liters per second (L/s) 4.4 lb/sec

Calculating the Required Power

The basic lift requirement is determined by the weight of the water to be lifted and the height difference. The equation for the energy required, without friction, is given by:

Energy (Flow rate (lb/sec) × Height (feet)) / 550

Substituting the known values:

4.4 lb/sec × 114.8 feet 505 ft lb/sec 0.918 HP

Estimating Frictional Losses

Frictional losses in the pipe need to be considered to determine the additional head that the pump must overcome. The formula for estimating frictional head loss is:

Hf (fL v2)/D2g

Where:

Hf Frictional head loss (feet) f Friction coefficient (typical range: 0.01 to 0.1) L Length of pipe (feet) v Flow velocity (feet per second) D Diameter of pipe (feet) g Acceleration due to gravity (32.2 ft/sec2)

Substituting the known values:

Hf (0.1 × 1312 × (3.22))/(0.1662) × 32.2 126.4 feet

Therefore, the additional power required due to friction is 556 ft lb/sec, which is equivalent to 1.01 HP.

Adding this to the initial lift requirement:

Total HP required 0.918 HP 1.01 HP 1.93 HP

Given that the 5.5 HP submersible pump is significantly more powerful than the 1.93 HP needed for this task, it should be capable of delivering the water even if it is not operating at its most efficient level.

Additional Considerations

One might wonder why the system uses 2-inch pipe in a system otherwise involving metric measures. Here are some observations:

Flow Rate Conversion

2 liters per second is equivalent to 32 gallons per minute (gpm).

System Breakdown

Pipe length is 1312 feet. Static head is 115 feet. Friction loss for the pipe is 25 feet. Total head is 140 feet.

The hydraulic horsepower (HP) required for the system can be calculated as:

Hydraulic HP (Flow rate in lb/sec × Head in feet) / 550

Substituting the known values:

4.4 lb/sec × 140 feet 616 ft lb/sec / 550 1.13 HP

Efficiency Considerations

Even if the pump operates at a low efficiency (e.g., 20%), it should still meet the needs of the system. Therefore, selecting a pump that can operate at a lower efficiency is entirely possible and would depend on the specific circumstances and requirements.

Conclusion

In conclusion, a 5.5 HP submersible pump can indeed deliver water to a location 400 meters away with a 35-meter elevation difference, even if it operates below its optimal efficiency. The system design, including the pipe size, flow rate, and distance, needs careful consideration, but with the right parameters, the task is achievable.