Using a nozzle opening of 2.5 inches, with a coefficient of discharge of 90% at 81 psi, what is the expected flow in gallons per minute?

To determine the expected flow in gallons per minute using the provided information, we can utilize the formula for flow through an orifice or nozzle, which is generally expressed as:

[ Q = C_d \times A \times \sqrt{2gh} ]

Where:

• ( Q ) is the flow rate in cubic feet per second (cfs).

• ( C_d ) is the coefficient of discharge.

• ( A ) is the cross-sectional area of the nozzle in square feet.

• ( g ) is the acceleration due to gravity (approximately 32.2 ft/s²).

• ( h ) is the hydraulic head in feet, which can be converted from psi.

First, we must convert the pressure from psi to feet of head (h). The conversion factor for water is approximately 2.31 feet of head per psi. Therefore:

[ h = 81 , \text{psi} \times 2.31 , \text{feet/psi} \approx 186.11 , \text{feet} ]

Next, we calculate the area of the nozzle. The diameter of the nozzle is 2.5 inches, so we first convert that to feet:

[ \