PSI to CFH for Water: Why Pressure Is Not Flow

A psi-to-cfh calculator for water cannot convert pressure alone into flow: psi measures pressure, while cfh measures volume flowing per hour. To estimate water flow in cubic feet per hour, you also need the pipe or opening geometry and the conditions affecting flow; this page’s calculator instead gives the ideal flow through a circular opening from pressure difference and opening diameter.

Formula

This estimate applies the ideal-orifice equation to water, then converts the resulting volume flow into cubic feet per hour (cfh). It assumes the pressure difference is across a sharp, circular opening and that losses from friction and turbulence are absent.

Q = 448.831 × π × (d / 24)² × √(2 × p × 144 / 62.4)

• Q is ideal flow in cubic feet per hour (ft³/h, also written cfh).
• d is opening diameter in inches. Dividing by 24 converts the diameter to a radius in feet.
• p is pressure difference across the opening in pounds per square inch (psi), converted to pounds per square foot by multiplying by 144.
• 62.4 is the approximate weight density of water in pounds per cubic foot under ordinary conditions.
• 448.831 converts cubic feet per second to cubic feet per hour: 3,600 seconds per hour.

The equation starts with the ideal exit speed, √(2ΔP/ρ), and multiplies it by the circular opening area, πr². In customary units, using water’s weight density gives the equivalent expression shown above. The second calculator result converts cfh to US gallons per minute (gpm), using approximately 7.48052 US gallons per cubic foot and 60 minutes per hour.

Worked Example

Using the calculator’s defaults—10 psi pressure difference and a 1-inch opening:

1. Convert pressure: 10 psi × 144 = 1,440 lb/ft².
2. Convert diameter to radius in feet: (1 / 12) / 2 = 1/24 ft.
3. Find opening area: π × (1/24)² ≈ 0.005454 ft².
4. Find ideal speed: √(2 × 1,440 / 62.4) ≈ 6.795 ft/s.
5. Multiply area by speed and convert seconds to hours: 0.005454 × 6.795 × 3,600 ≈ 133.33 ft³/h.

The calculator therefore returns 133.33 cfh and approximately 0.30 US gpm. These are idealized values, not a prediction that a real pipe or fitting will deliver that flow.

Why PSI Alone Cannot Determine CFH

Pressure describes force per area; flow describes how much volume passes a point over time. A pressure reading does not specify the size of the route the water can take. At the same pressure difference, a small opening and a large opening can pass very different amounts of water. Pipe length, internal diameter, bends, valves, surface roughness, fittings, and the outlet condition also affect actual flow.

It matters whether a pressure value is gauge pressure or absolute pressure, too. Flow through a restriction depends on the pressure difference between its upstream and downstream sides, not merely a pressure reading at one location. For an outlet discharging to the atmosphere, upstream gauge pressure may approximate that difference; otherwise, both pressures are needed. Do not treat a static pressure reading as a flow measurement.

How to Use This Estimate

• Enter the pressure drop across the opening, in psi. Use a nonnegative value; zero pressure difference gives zero ideal flow.
• Enter the opening’s actual diameter in inches, not the nominal size printed for a pipe. Nominal pipe size is not necessarily its inside diameter.
• Read the first result as ideal cubic feet per hour. The second result is the same estimated flow expressed in US gallons per minute.
• For metric context, 1 cubic foot is about 0.0283168 cubic metres, and 1 US gallon is about 3.78541 litres. Thus, 1 cfh is about 0.47195 litres per minute.

The result scales with the square of the opening diameter and with the square root of pressure difference. For example, doubling the diameter multiplies ideal flow by four; quadrupling the pressure difference doubles ideal flow. This relationship is useful for understanding trends, but it does not capture losses in a real system.

Limits and Common Mistakes

The calculator is an ideal-orifice estimate, not a general pipe-flow calculator. Real flow is usually lower because energy is lost through contraction, friction, turbulence, valves, and fittings. A sharp-edged opening also behaves differently from a long tube or a rounded nozzle. For piping systems, a suitable engineering calculation or direct flow measurement is needed; the necessary information can include pipe material, length, inside diameter, fittings, elevation change, and water temperature.

• Confusing cfh and gpm: cfh means cubic feet per hour. The calculator’s second output is US gallons per minute, not imperial gallons per minute.
• Entering nominal pipe size: use the measured or specified internal opening diameter when applying the orifice model.
• Using pressure instead of pressure difference: subtract downstream pressure from upstream pressure. A single gauge reading is not always the required value.
• Ignoring units: the calculator accepts psi and inches. A diameter in millimetres or pressure in kPa must be converted first.
• Overreading precision: two decimal places are arithmetic presentation, not evidence that a real installation can be predicted to that accuracy.

For a system where water is flowing through a pipe rather than a simple opening, use a method designed for pipe friction and the actual system layout. If the application depends on a reliable flow or pressure rating, confirm the calculation and measurements with a qualified professional.

Frequently Asked Questions

Can I convert psi directly to cfh?
No. Psi is pressure and cfh is volume flow. You need additional information, especially the passage geometry and the pressure difference across it.

How many cfh is 1 psi of water pressure?
There is no single answer. Flow at 1 psi depends on the opening or pipe dimensions and on losses in the system. The calculator can estimate ideal flow only after you provide an opening diameter.

Is this calculator suitable for a whole water pipe?
Not by itself. It models an ideal circular opening, not friction along a pipe, bends, valves, or changes in elevation. Use a pipe-flow method for a complete piping run.

Does a higher psi always mean more water flow?
For the same opening and conditions, a greater pressure difference increases ideal flow. In a real installation, restrictions and system behavior determine how much flow actually changes.

What does cfh mean?
CFH means cubic feet per hour, a volumetric flow rate. It is not the same unit as cubic feet per minute (cfm), gallons per minute (gpm), or pressure in psi.

Related

• Evaporation Rate Formula and How to Calculate It
• Boiling Water Evaporation Rate Calculator Formula
• Atmospheric Pressure from Elevation and Angle

in p | Pressure difference | psi | 10 | 0
in d | Opening diameter | in | 1 | 0
out q | Ideal water flow | ft^3/h | 448.831 * pi * (d / 24)^2 * sqrt(2 * p * 144 / 62.4) | 2
out g | Ideal water flow | gal/min | 448.831 * pi * (d / 24)^2 * sqrt(2 * p * 144 / 62.4) / 7.48052 / 60 | 2