Orifice plates are one of the oldest and most widely used flow-measurement devices in industrial piping: install a plate with a precisely sized hole, measure the pressure drop across it, and the flow rate follows directly from Q = Cd·A·√(2ΔP/ρ). The formula looks like a straightforward rearrangement of Bernoulli's equation, and it is — the only wrinkle is the discharge coefficient Cd, which quietly does the work of correcting an idealized prediction for how real fluids actually behave.
How the Orifice Flow Calculator works
The calculator applies Q = Cd·A·√(2ΔP/ρ) directly on the Flow Rate tab: the discharge coefficient Cd times the orifice area A, times the square root of 2 times the pressure difference ΔP divided by the fluid density ρ. The Solve tab rearranges the same equation to isolate the orifice area or the pressure difference given a target flow rate and the other three values. The Discharge Coefficient tab runs the equation in reverse — given a flow rate you've actually measured, it isolates Cd, letting you calibrate a real orifice rather than assume a textbook value.
Inputs and what they mean
The discharge coefficient Cd is dimensionless and, for a standard sharp-edged (thin-plate) orifice, typically falls between 0.60 and 0.65 — round, well-machined nozzles and venturis can reach 0.95-0.98 because they avoid the sharp vena-contracta losses of a plain hole in a plate. Orifice area A (m²) is the cross-sectional area of the hole itself, not the pipe it sits in. Pressure difference ΔP (Pa) is the drop measured across the orifice, usually with taps just upstream and downstream. Fluid density ρ (kg/m³) is a property of the fluid — water is about 1,000 kg/m³, while gases vary enormously with pressure and temperature. Of these, ΔP has the gentlest effect on the result: because flow depends on its square root, doubling the pressure drop only increases flow by about 41%, not 100%.
Limits and edge cases
This formula assumes steady, incompressible flow of a Newtonian fluid, and a discharge coefficient that's either known from a standard reference (ASME/ISO orifice-plate tables) or independently calibrated — the calculator does not derive Cd from geometry alone, since real Cd values depend on Reynolds number, tap location, and manufacturing tolerances in ways a single formula can't fully capture. For compressible gas flow across a large pressure ratio, an additional expansibility (Y) factor is normally applied on top of Cd, which this calculator does not include. Treat results here as a solid engineering estimate for liquid flow and low-pressure-ratio gas flow, and consult an ASME/ISO flow-measurement standard for precision metering applications.