When using the condensed Q formula, what is the approximate friction loss in 600 feet of 3-inch hose flowing 500 gpm?

The condensed Q formula is a practical tool used in firefighting to estimate friction loss in hoses based on their diameter, flow rate, and length. The formula is represented as:

Friction Loss (psi) = Q² × L / C

Where:

• Q = Flow rate in hundreds of gallons per minute (gpm)

• L = Length of the hose in hundred feet

• C = A coefficient that depends on the diameter of the hose

For a 3-inch hose, the common coefficient (C) used is typically 15.

In this case:

• The flow rate is 500 gpm, which translates to Q = 5 (since we express it in hundreds).

• The length of the hose is 600 feet, or L = 6 (when also expressed in hundreds).

Plugging these values into the formula yields:

Friction Loss = (5²) × 6 / 15

= 25 × 6 / 15

= 150 psi

Thus, the approximation of 150 psi is derived from applying the correct values into the condensed Q formula based on the specified hose dimensions and flow rate. This calculation captures the essence of how friction loss increases as flow rate and hose length increase