Input parameters
Example data table
This example table shows typical flows for a one inch pipe using the Bernoulli based method with water at standard conditions.
| Upstream pressure P1 (psi) | Downstream pressure P2 (psi) | Pipe inner diameter (inches) | Estimated flow (GPM) |
|---|---|---|---|
| 30 | 0 | 1.0 | 28.8 |
| 50 | 0 | 1.0 | 37.2 |
| 80 | 0 | 1.0 | 47.0 |
Formula used
For the Bernoulli mode the calculator assumes an incompressible fluid at constant elevation and negligible tank velocity. The flow velocity is estimated from the pressure difference using:
v = √(2 × ΔP × 144 / ρ)
where ΔP is the pressure difference in psi, ρ is fluid density in lb/ft³ and 144 converts psi to lb/ft².
The volumetric flow rate in gallons per minute is then:
QGPM = v × A × 7.48052 × 60, where A is the pipe cross-sectional area in ft².
In nozzle K-factor mode, flow is estimated with the standard sprinkler relationship
QGPM = K × √PSI, using the K-factor supplied by the manufacturer.
How to use this calculator
- Select the calculation mode: Bernoulli for pipe based flow, or nozzle K-factor for sprinkler style devices.
- Enter pressures in psi. For gauge style readings, use zero downstream pressure for atmospheric discharge.
- Specify pipe inner diameter in inches and fluid density if different from water.
- Press Calculate flow rate to view the estimated gallons per minute.
- Review the calculation summary, then export the numbers to CSV or simple text based PDF for reporting.
Understanding PSI and GPM in pressurised piping
PSI describes the pressure driving water through a pipe, while GPM expresses how much volume passes a section each minute. Higher pressure usually increases flow, but pipe diameter, roughness and layout strongly influence the final GPM value.
Pressure conversion alongside flow calculations
Many systems are specified in bar or atmospheric units rather than psi. You can use the dedicated Bar to PSIG Converter to convert bar readings into gauge pressure before estimating GPM with this tool.
Relating PSI to atmospheric pressure
When sizing tanks or vents, it is helpful to compare gauge pressure with atmospheric pressure. The separate psi to atm conversion calculator converts between psi and atmospheres, complementing the flow based calculations done here.
Impact of pipe diameter on flow rate
Flow rate scales with pipe cross-sectional area. Doubling diameter increases area by a factor of four and can dramatically increase GPM for the same pressure difference. Use this calculator to compare scenarios with different diameters quickly.
Using nozzle K-factors for fast estimates
Sprinkler and nozzle datasheets often provide a K-factor in units of GPM per square root of PSI. Enter this K-factor with the operating pressure to estimate GPM instantly without detailed pipe modelling.
Limitations and engineering judgement
The calculator assumes steady flow, clean water and negligible pipe losses beyond the selected method. Real installations may require additional safety margins, manufacturer curves or hydraulic analysis, especially for long pipe runs or viscous fluids.
Frequently asked questions
1. Which mode should I use for most water pipes?
For typical tanks, manifolds and distribution pipes, the Bernoulli mode is usually more appropriate. It considers upstream and downstream pressures together with pipe diameter, giving a physically consistent estimate of velocity and GPM.
2. When is the nozzle K-factor method preferable?
Use the K-factor method for spray nozzles, sprinklers or fire fighting tips where the manufacturer supplies a K value. It is ideal when you mainly need GPM at a known nozzle pressure.
3. Can this calculator convert pressure units like bar or atmospheres?
This page focuses on flow from psi based inputs. To convert between psi and atmospheres, first use the dedicated psi to atm conversion page, then return here with the required psi value.
4. Does pipe length or roughness affect the GPM result?
Yes, friction over long or rough pipes reduces GPM. This calculator approximates ideal conditions, so real systems may show lower flow. For critical designs, combine these results with detailed hydraulic loss calculations or manufacturer data.
5. What fluid density should I use for liquids other than water?
Keep density in lb per cubic foot. Obtain the liquid density from datasheets or handbooks, convert to lb/ft³ if necessary, and enter it in the Bernoulli section. Higher density reduces velocity and therefore lowers GPM.
6. Why does doubling pressure not exactly double the GPM?
In both Bernoulli and nozzle K-factor approaches, flow depends on the square root of pressure difference. Doubling pressure increases GPM by about forty percent, while quadrupling pressure roughly doubles GPM, assuming other parameters stay constant.
7. How accurate are the CSV and PDF exports?
The exports contain the same rounded numbers displayed in the calculation summary. They are intended for quick design notes, reports or sharing with colleagues and should be accompanied by engineering checks for final system approval.