If Engine 1 is on a hydrant supplying 600 ft of 5-inch hose to Engine 2, which is pumping 1200 gallons/min, what is the pump discharge pressure, calculated using the Q formula?

To calculate the pump discharge pressure when using the Q formula, it's essential to first understand the relationship between flow rate, hose diameter, and pressure loss.

The Q formula is expressed as:

[ Q = \frac{{\text{C}} \cdot \text{D}^2 \cdot \text{P}}{100} ]

Where:

• ( Q ) is the flow rate in gallons per minute (gpm),

• ( C ) is a constant depending on the material and condition of the hose (for a standard fire hose, this can be taken as approximately 0.2 for calculation purposes),

• ( D ) is the diameter of the hose in inches,

• ( P ) is the pressure in psi.

In this scenario, you have the following information:

• Engine 2 is pumping 1200 gallons per minute (gpm),

• The hose diameter is 5 inches,

• The length of the hose is 600 feet.

To calculate the pressure required at the pump discharge, you have to account for the flow and the friction loss through the 5-inch hose over that distance. The friction loss formula for a smooth bore hose is often approximated as:

[ \text{F