How this calculation works
Continuity links the two average velocities. At equal elevation, the ideal Bernoulli pressure difference supplies their kinetic-energy difference. Apply the separately entered flow coefficient to the ideal flow.
Q = Cd·A₂√[2Δp/(ρ(1−β⁴))], β = d₂/d₁A worked example
For upstream diameter 100 mm, throat 50 mm, pressure difference 1,000 Pa, density 1,000 kg/m³ and Cd = 1, the model gives about 172.0721 L/min.
Good to know
Steady incompressible equal-elevation model. The differential pressure is not permanent pressure loss. This does not supply a standardized meter calibration, gas expansibility, cavitation check or uncertainty budget.
Reference: OpenStax: Bernoulli’s equation (opens in a new tab) ↗
A narrower throat has a higher mean speed
For incompressible flow, volume flow is the same upstream and at the throat. A 50 mm throat has one quarter the area of a 100 mm upstream section, so its mean speed is four times higher at the same volume flow.
At equal elevation, ideal Bernoulli flow links the increase in kinetic energy to a decrease in static pressure. The formula combines that relation with continuity to solve Q from the upstream-to-throat static pressure difference.
The pipe flow calculator checks that both sections carry the same volume per second despite their different average speeds.
Calibration adjusts the ideal relationship
The displayed ideal flow corresponds to Cd = 1. An independently supplied coefficient scales it to a hypothetical calibrated flow. The tool does not choose a standards-based coefficient from a diameter or meter name.
The pipe flow calculator can verify each section’s Q = Av relation. Both verification rows should give the same volume flow even though the section speeds differ. This is a continuity check, not a pressure-recovery calculation.
Differential pressure is not permanent pressure loss
Some static pressure can recover as flow slows after the throat. The entered tap difference therefore must not be treated automatically as irreversible downstream loss. The Darcy Weisbach pressure loss calculator addresses an explicit friction-loss model separately.
The page assumes equal tap elevation and constant density. Gas expansion, cavitation, detailed pressure-tap geometry and measurement uncertainty are outside the model. When throat and upstream diameters are nearly equal, small diameter errors strongly affect the calculated flow.
A few questions, answered
Must the throat be smaller?
Yes. This form requires a positive area contraction with throat diameter below upstream diameter.
What if the pressure difference is zero?
The modeled flow is zero.
Does Cd = 1 mean a real meter has no uncertainty?
No. It is an ideal coefficient assumption and says nothing about actual calibration or measurement uncertainty.