In short: water forced through a ½-inch sharp-edged opening by 40 psi discharges at roughly 28.8 GPM (1.82 L/s). Flow rate rises with the square root of pressure and with the square of the opening's diameter — use the calculator above for any combination of the two.
These figures are planning aids based on the orifice equation. For nozzle, valve or metering specifications, confirm with the manufacturer's rated discharge coefficient.
How to calculate flow rate from pressure
When water is pushed through an opening by a pressure difference, the pressure converts into velocity, and velocity through a known area gives a flow rate. That relationship is the orifice form of Torricelli's equation:
The calculator converts your pressure to pascals and your diameter to an area in square meters, computes the theoretical velocity from √(2ΔP/ρ), scales it down by the discharge coefficient to account for real-world losses at the edge of the opening, and multiplies by area to get flow rate.
Worked example. Take the default case: a ½-inch (0.0127 m) sharp-edged opening under 40 psi (275,790 Pa) of water at 20°C, density 998.20 kg/m³. The opening's area is 0.0001267 m². Velocity is √(2 × 275,790 / 998.20) = 23.51 m/s. Flow rate is 0.61 × 0.0001267 × 23.51 = 0.001816 m³/s, which converts to 28.79 GPM — matching the calculator's default result.
Why the square root? Doubling the pressure differential does not double the flow rate. Because velocity depends on the square root of pressure, doubling ΔP only increases flow by a factor of √2, about 41%. To double the flow rate at a fixed opening, you would need roughly four times the pressure.
Why opening size matters more than pressure
Flow rate scales with area, and area scales with the square of diameter. A ¾-inch opening has 2.25 times the area of a ½-inch opening, so at the same pressure it passes 2.25 times the flow — while a pressure increase of the same ratio would only add about 50% more flow. That is why, when someone asks for more water, the practical fix is usually a bigger opening rather than more pressure.
The discharge coefficient (Cd) corrects the idealized velocity for real losses at the edge of the opening. A sharp, thin-plate hole (Cd ≈ 0.61) contracts the jet as it exits and loses more energy than a smoothly rounded, bell-mouth entrance (Cd ≈ 0.98), which lets water follow the opening's shape with far less turbulence. A short tube or nozzle sits in between, around 0.80. Use the manufacturer's rated Cd for a specific nozzle or valve whenever it is available — see our orifice flow calculator if you already know a head (in feet or meters) instead of a pressure.
Flow rate by opening diameter
Flow rate at a fixed 40 psi differential, sharp-edged opening (Cd 0.61), fresh water at 20°C. Notice how flow roughly quadruples each time the diameter doubles.
| Diameter | Flow rate (GPM) | Flow rate (L/s) |
|---|---|---|
| 1/8″ (0.125 in) | 1.80 | 0.114 |
| 1/4″ (0.25 in) | 7.20 | 0.454 |
| 3/8″ (0.375 in) | 16.20 | 1.022 |
| 1/2″ (0.5 in) (default) | 28.79 | 1.816 |
| 5/8″ (0.625 in) | 44.99 | 2.838 |
| 3/4″ (0.75 in) | 64.78 | 4.087 |
| 1″ (1.0 in) | 115.17 | 7.266 |
Flow rate by pressure
Flow rate through a fixed ½-inch sharp-edged opening (Cd 0.61), fresh water at 20°C, across a range of supply pressures.
| Pressure | Flow rate (GPM) | Velocity (ft/s) |
|---|---|---|
| 10 psi | 14.40 | 38.6 |
| 20 psi | 20.36 | 54.5 |
| 30 psi | 24.93 | 66.8 |
| 40 psi (default) | 28.79 | 77.1 |
| 60 psi | 35.26 | 94.5 |
| 80 psi | 40.72 | 109.1 |
| 100 psi | 45.52 | 121.9 |
Worked examples
Garden hose nozzle
19.8 GPM
A 3/8-inch nozzle opening under 60 psi hose pressure discharges about 19.8 GPM (75.1 L/min) with a sharp-edged Cd of 0.61 — typical of an adjustable spray nozzle wide open.
Pressure washer nozzle
0.73 GPM
A tiny 0.03-inch nozzle orifice at 2,000 psi — typical of a pressure washer tip — passes only about 0.73 GPM (2.8 L/min). High pressure through a small opening still means modest flow.
Pressure relief port
39.7 GPM
A 3/4-inch relief port opening under a modest 15 psi discharges about 39.7 GPM (150.2 L/min) — low pressure can still move a lot of water through a large opening.
What else affects the result
Water temperature. Warmer water is slightly less dense, so it flows a little faster through the same opening at the same pressure. Heating water from 20°C to 60°C increases flow rate by less than 1% — real, but small enough to ignore outside precise lab or dosing work.
Dissolved salts. Seawater is denser than fresh water, so it flows slightly slower for the same pressure and opening — about 1.3% less at 20°C for a typical 35 g/kg salinity. Use the water type selector in the advanced options if you are working with brine or seawater.
Upstream and downstream conditions. This calculator assumes the pressure differential is measured right across the opening, with a large reservoir or pipe upstream so approach velocity is negligible. It does not model friction along a length of pipe leading up to the opening — for that, see the friction loss calculator or the pressure loss calculator.
Frequently asked questions
What is the formula for flow rate from pressure?
For water discharging through an opening, Q = Cd · A · √(2·ΔP/ρ), where Q is flow rate, Cd is the discharge coefficient of the opening, A is its cross-sectional area, ΔP is the pressure differential across it, and ρ is water density. This is the orifice form of Torricelli's equation.
How does opening diameter affect the flow rate?
Flow rate scales with the square of the diameter, because area scales with diameter squared. Doubling the diameter of an opening roughly quadruples the flow rate at the same pressure, since the area increases four-fold while velocity stays the same.
Does doubling the pressure double the flow rate?
No. Flow rate scales with the square root of pressure, not pressure itself. Doubling the pressure differential increases flow rate by a factor of about 1.41 (√2), roughly a 41% increase, not 100%.
What discharge coefficient (Cd) should I use?
Use about 0.61 for a sharp-edged opening such as a thin plate orifice or a drilled hole, about 0.80 for a short tube or nozzle, and about 0.98 for a smoothly rounded, bell-mouth entrance. If you know the manufacturer's rated Cd for a specific nozzle or valve, use that instead.
Does water temperature change the flow rate?
Only slightly. Warmer water is less dense, so it flows a little faster through the same opening at the same pressure. Heating water from 20°C to 60°C increases flow rate by less than 1%, which is usually too small to matter outside precise lab work.
Does this calculator account for pipe friction?
No. This tool models flow through a discrete opening — a nozzle, orifice, valve port or drilled hole — driven directly by the pressure differential across it. It does not include friction losses along a length of pipe. For that, use the friction loss or Hazen-Williams calculator.
Sources & references
- Torricelli, E. (1643). De motu gravium naturaliter accelerato — the founding relation between fluid velocity and driving head.
- ISO 5167-1:2022. Measurement of fluid flow by means of pressure differential devices.
- Crane Co. (2013). Flow of Fluids Through Valves, Fittings, and Pipe (Technical Paper 410).
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)