Introduction and Specifications

This conceptual ranch has 1400 head of cattle and needs to supply 27 acre-feet of water per year. The nearest well is 4 miles away from a tall hill, to which the ranchers would like to pump water so it can be gravity-fed to the rest of the ranch. The 1400 foot-deep well has a submersible pump at 1375 feet (which pumps through a 2" schedule 80 galvanized steel column), and has a static water level at 1325 feet deep. The elevation rise from the well head to the hill is 600 feet. 

There is no local electricity at the ranch, so a 20 kW diesel motor will supply power to the pump, which will cost about $0.25/kWh to run. Determine the pump impeller size, speed, and the PVC line size. Assume that maintenance cost on the pipe to be a tenth of the total pipe cost, per year.

Solution

A detailed spreadsheet is attached at the end of the solution for all complete computational details. First, it was necessary to find the required pump head to send the water from the well to the hill. Using the general fluids energy equation, the pump head was found, which was plotted against the necessary volume flow rate as the system curve. Next, five different pump speeds and impeller sizes were compared and plotted. Optimally, the best selections are where the pump and system curves intersect.

Before selecting one pump size, the combined energy, pump, and pipe costs were compared. As it turned out, the pipe diameter was the largest contributing factor to 10-year cost, far ahead the cost of energy. 

Thus, the 2" diameter pipe sized proved to be the most cost-effective option. When finding the volume flow rate through the pipe for this diameter, based on RPM and impeller size, it was discovered that the pump would need to run for 22.5 hours per day. 

Below is the spreadsheet with all calculations: