If you had a pumping arrangement with a pump pumping water uphill 300' at a rate of 950 GPM with a constant pressure of 50 PSI at the top, what would the discharge pressure be?

To determine the discharge pressure in a pumping arrangement where water is pumped uphill to a height of 300 feet at a rate of 950 gallons per minute (GPM), it's essential to consider the height the water has to be lifted, the density of water, and the pressure at the discharge point.

The increased pressure from lifting water can be calculated using the formula that relates the height (in feet) to the pressure (in PSI). The hydraulic pressure exerted due to the elevation can be calculated using the hydraulic formula:

[ \text{Pressure (PSI)} = \frac{\text{Height (feet)} \times \text{Density of water (lbs/ft³)}}{144} ]

Where the approximate weight density of water is 62.4 lbs/ft³.

Now, if we calculate the pressure required to lift the water 300 feet:

1. Convert the height to pressure:

[

\text{Hydraulic Pressure} = \frac{300 , \text{feet} \times 62.4 , \text{lbs/ft}^3}{144 , \text{in}^2} = 130.0 , \text{PSI}