Nozzle Flow Rate Calculator
Water flow through a nozzle or orifice from diameter and pressure — Q = 29.84 × Cd × d² × √P (gpm) with metric output — for fire hoses, pressure washers, irrigation and hydrants, with reaction force and velocity.
How it works
Q = Cd × A × √(2P/ρ); in US units Q (gpm) = 29.84 × Cd × d² (in) × √P (psi); reaction ≈ ρ Q v; velocity = √(2P/ρ)
A nozzle turns pressure into velocity — Bernoulli says the jet speed is the square root of twice the pressure over density, about 37 m/s at 7 bar regardless of nozzle size — and flow is that velocity times the opening area, trimmed by a discharge coefficient that accounts for the jet contracting and for friction. Smooth tapered fire nozzles approach an ideal 0.97; a sharp-edged hole in a plate manages only 0.61. The fire-service form of the equation, 29.84 × Cd × d² × √P, is the same physics in inches, psi and gallons and is used for hydrant flow tests and hose-line planning. The momentum leaving the nozzle produces an equal backward push — the reaction force that makes large hand lines a two-person job.
Worked example
A 15 mm smooth-bore nozzle (Cd 0.97) at 7 bar: jet 37.5 m/s, flow ≈ 385 L/min (102 gpm), reaction about 240 N.
Frequently asked questions
What pressure should a smooth-bore fire nozzle run at?
Typically 50 psi (3.4 bar) for hand lines and 80 psi (5.5 bar) for master streams — the tables in fire-service hydraulics assume those.
How do I measure hydrant flow?
Read the pitot pressure at the outlet, look up the outlet’s coefficient (0.9 smooth rounded, 0.8 square, 0.7 protruding) and apply the same formula with the outlet diameter.
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This calculator is for educational purposes. Double-check important results before acting on them.