The formula (29.7)(d^2)(sqrt NP) is used to estimate the gallons per minute in what type of nozzle?

• A. Flow velocity
• B. Head loss
• C. Pressure drop
• D. Gallons per minute in a smooth bore nozzle

Answer: (D)

The main idea is that discharge through a smooth bore nozzle scales with the bore area and with the available pressure. The flow rate in gallons per minute is roughly the cross-sectional area of the nozzle (which is proportional to the square of the diameter) times the jet velocity, and the velocity produced by a given nozzle pressure grows with the square root of that pressure. Put together, Q ∝ d^2 × sqrt(NP). The constant 29.7 converts units so that with diameter in inches and nozzle pressure in psi, the result comes out in gallons per minute. That’s why this formula is used specifically for estimating gallons per minute in a smooth bore nozzle. It isn’t the right form for flow velocity, and it doesn’t express head loss or pressure drop in the system, which follow different relationships.