Exit speed, flow rate and jet force from pressure or head — with the limit for gases.
Liquids only. Water 1,000 kg/m³ (62.3 lb/ft³).
Rounded nozzle 0.97–0.99. A sharp-edged orifice is also about 0.98: its loss is in the contraction below.
Empty = 1, a rounded nozzle. A sharp-edged orifice is about 0.62.
Liquids only. Empty = a large inlet with no approach speed.
Empty = standard atmosphere.
A high-pressure jet can injure skin and throw an unsecured hose or lance; follow the equipment maker's limits.
Example Result
Your result will appear here
The calculated result will appear here after you press Calculate.
A nozzle turns pressure into speed. Ignoring losses, the exit velocity of a liquid depends only on the pressure drop and the density: v = √(2ΔP ÷ ρ). Water falling through a head h leaves at the same speed a stone would reach falling that distance, v = √(2gh), which is Torricelli's result. Enter the pressure drop or the head, the fluid, the exit diameter and a velocity coefficient, and the calculator returns the exit speed, the flow rate and the reaction force on the nozzle. Add the inlet diameter when the pipe is not much larger than the nozzle. For air and other gases the calculator switches to compressible flow and stops at the speed of sound at the throat, which is as fast as a converging nozzle can go.
Choose Pressure or Head, and the fluid.
Enter the pressure difference across the nozzle, or the head of liquid above it.
For a liquid, enter its density. For a gas, enter its temperature.
Enter the exit diameter and the velocity coefficient.
Add a contraction coefficient for a sharp-edged hole, and an inlet diameter if the pipe is close to the nozzle size.
Press Calculate for the exit speed, the flow and the jet force.
By O.E. — Partner, chairman of the board and CEO of a metal products manufacturer for 21 years; the company exports to 45 countries.
Drafted with AI assistance; calculations checked against primary sources and tested with the site's own code. About FlowUtil
Last reviewed
Pressure and head are the same thing in different units: 200 kPa of water is a head of 20.4 m.
| Symbol | Meaning |
|---|---|
| v | Exit speed: Cv √(2ΔP ÷ ρ), or Cv √(2gh) for a head of liquid |
| Q | Flow: Cc × v × π d² ÷ 4. Cc = 1 for a rounded nozzle |
| F | Reaction force: ρ Q v, what the hose or mount must resist |
| Cv, Cc | Velocity and contraction coefficients |
1Water, 200 kPa, 10 mm nozzle, Cv 0.97.
√(2 × 200,000 ÷ 1,000) = 20.0 m/s; × 0.97; area 78.54 mm²; 1,000 × 0.00152 × 19.4
19.4 m/s, 1.52 L/s (5.49 m³/h), 29.6 N of reaction
Oil with a density of 870 kg/m³ at 500 kPa through a 6 mm nozzle (Cv 0.95) leaves at 32.2 m/s, carrying 0.91 L/s.
2A 1⅛ in smooth-bore tip at 50 psi. Fire services use gpm = 29.7 × d² × √P.
29.7 × 1.266 × 7.07; reaction 1.57 × d² × P
266 gpm, 99 lbf
The velocity formula agrees: 50 psi of water gives 86 ft/s, or 267 gpm through that tip. That reaction is why handlines need a firm grip.
The formulas above assume the fluid approaches the nozzle slowly. If the inlet is narrow, the fluid already has speed, and for the diameter ratio β = d ÷ D the exit velocity rises by 1 ÷ √(1 − β⁴). Below a ratio of about 0.4 the correction can be ignored.
| d ÷ D | Increase in velocity |
|---|---|
| 0.2 | 0.1% |
| 0.4 | 1.3% |
| 0.6 | 7.2% |
| 0.8 | 30% |
Both produce a fast jet, and the difference shows up in the flow, not the speed. In a sharp-edged hole the jet keeps contracting after it leaves, to about 62% of the hole's area. Its velocity is still about 98% of ideal, but the flow is only about 61% of ideal. A rounded nozzle has almost no contraction, so it passes about 97% of ideal. Enter the velocity coefficient for speed, and the contraction coefficient for flow.
Gas expands as it accelerates, so v = √(2ΔP ÷ ρ) is only a low-speed approximation, fair below about Mach 0.3, roughly 100 m/s in air. The calculator uses compressible flow for gases: at 5 kPa, air leaves at 87 m/s, Mach 0.26.
Push harder and the flow reaches the speed of sound at the throat. For air this happens when the upstream absolute pressure is about 1.89 times the downstream pressure, and raising the upstream pressure further no longer raises the exit speed of a converging nozzle. At 200 kPa gauge into the atmosphere the simple formula would claim 560 m/s; the real limit at 20 °C is about 313 m/s, and that is the speed the calculator reports, with a warning.
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