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Ideal Water Opening Flow from Pressure Drop

Estimate ideal water flow from upstream and exit pressures plus circular opening size, with reversible pressure, area and flow relationships.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

With a 10 psi pressure difference and a 1 inch circular opening, this ideal-water model gives about 94.33 US gal/min before friction or discharge losses.

Q = A × √(2g × 144 × ΔP / 62.4) × (60 × 1728 / 231), with A in ft² and ΔP in psi

Worked example

Enter these known values and leave the other values blank.

Upstream absolute pressure
24.7 psi
Exit absolute pressure
14.7 psi
Circular opening diameter
1 in
Opening cross-sectional area
0.7854 in²
Ideal water volume flow
94.33 US gal/min

Assumptions and limitations

  • This is an ideal steady, incompressible water-flow estimate using the captured 62.4 lb/ft³ water weight density and 32.174 ft/s² gravity. It assumes negligible upstream velocity and no elevation term.
  • Friction, pipe length, bends, viscosity effects and discharge coefficients are absent. The answer is not a measured flow or a complete pipe-sizing calculation.
  • Use positive absolute pressures on the same basis, with upstream pressure greater than exit pressure. The default exit pressure is 14.7 psi absolute; do not pair it with an unconverted gauge-pressure reading.
  • The opening is circular when diameter is used. Enter area directly for an equivalent ideal opening. A US liquid gallon contains exactly 231 cubic inches.

Common questions

Can pressure alone determine gallons per minute?

No. Opening area and a flow model are also needed. Real systems additionally depend on losses and geometry; this calculator supplies an ideal estimate under its stated assumptions.

References

Bookify replaces the rounded 448.83 flow factor with the exact 60 × 1728 / 231 cubic-feet-per-second to US-gallons-per-minute ratio, updating every retained inverse consistently. Bookify requires positive flow in this positive-pressure-drop model. Volumetric flow rates use exact US or imperial fluid-volume definitions and exact seconds per minute, hour and day. US gallons per minute use exactly 0.003785411784 cubic meters per gallon and 60 seconds per minute. Pounds-force per square inch use the exact international pound and inch with standard gravity, replacing the rounded captured factor.

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