Hong Life CalculatorsUnderstanding the PSI to GPM calculator — concept and principle
This calculator estimates the flow from a nozzle or orifice from the pressure at the opening and its diameter, using the orifice equation with a discharge coefficient. It gives the flow in US gallons per minute, litres per minute and cubic metres per hour, the jet velocity and the fire-service rule of thumb for comparison. Firefighters, irrigation designers and plumbers use it.
How it is calculated
Jet velocity v = √(2 Δp ÷ ρ)
Q = C_d × (π/4) d² × v
Fire-service rule: GPM ≈ 29.7 × d² × √P (d in inches, P in psi)
- Water density 62.4 lb/ft³ × specific gravity; 1 psi = 6,894.757 Pa; 1 US gal = 231 in³.
The principle
Bernoulli's principle says that pressure energy turns into kinetic energy as liquid leaves an opening. The speed depends only on pressure and density, and the flow is that speed times the area of the jet. Real jets are slightly narrower and slower than ideal, which the discharge coefficient corrects for: smooth-bore nozzles are close to 1, sharp-edged holes much lower. For water, the constants combine to about 29.8 × C_d × d² × √P.
Worked example
Default inputs: 50 psi, 1 inch nozzle, C_d = 0.995, specific gravity 1.
- v = √(2 × 50 × 6,894.757 ÷ 999.6) = 86.2 ft/s.
- Theoretical flow with C_d = 1 = 210.9 gal/min.
- With C_d = 0.995: 209.9 gal/min = 794 L/min = 47.67 m³/h.
- Fire-service rule: 29.7 × 1² × √50 = 210 gal/min.
| Nozzle or orifice diameter (inches) | Flow rate (US gal/min) |
|---|---|
| 0.25 | 13.1 |
| 0.5 | 52.5 |
| 0.75 | 118.1 |
| 1 | 209.9 |
| 1.25 | 327.9 |
| 1.5 | 472.2 |
| 2 | 839.5 |
How to read the result
Flow rises with the square of diameter but only with the square root of pressure, so a slightly larger nozzle adds much more flow than more pressure. Use the pressure at the nozzle; losses in long hoses or pipes reduce it well below the pump pressure.
Common mistakes
- Using pump pressure instead of nozzle pressure.
- Using C_d = 1 for a sharp-edged orifice, whose C_d is much lower.
- Mixing inches and millimetres.
Frequently asked questions
Why does doubling the pressure not double the flow?
Flow depends on the square root of pressure, so doubling pressure raises flow about 41%.
What is the discharge coefficient?
The ratio of actual to ideal flow, accounting for jet contraction and friction.
Where does 29.7 come from?
It combines the constants of the orifice equation for water with a typical smooth-bore C_d.
Does this include hose friction?
No. Enter the pressure at the opening.
Sources: Utah Valley University Fire & Rescue Academy, "Friction Loss and Nozzle Flow Reference" · Orifice equation from Bernoulli's principle (standard fluid mechanics)