Orifice Flow Calculator (Discharge Through an Orifice)
Flow rate through a sharp edged orifice from the pressure difference across it, using the incompressible orifice equation with the velocity of approach correction that accounts for the fluid upstream already moving towards the hole. Results include the mass flow rate, the velocity in the orifice and in the approach pipe, the diameter ratio, and the head loss.
How to use this calculator
- Enter the orifice bore, the upstream pipe diameter, and the pressure difference measured across the orifice from a tap upstream to one at the vena contracta.
- Enter the discharge coefficient for the type of opening, which is about 0.62 for a sharp edged plate in a pipe and about 0.98 for a rounded entry.
- Enter the fluid density. For a gas, note that the expansion across the orifice also matters and is not covered here.
- Read the volumetric and mass flow rates, the velocity of approach factor, and the head loss, then check the diameter ratio is inside the range where the coefficient is reliable.
Frequently asked questions
Why is the discharge coefficient only about 0.62 for a sharp edged orifice?
The jet contracts after it leaves the plate, reaching its smallest section, the vena contracta, some distance downstream at roughly 62 percent of the geometric hole area for a sharp edge. The coefficient bundles that contraction together with the friction losses, so the calculation uses the full bore area and corrects for the real flow area with a single number. Rounding the entry reduces the contraction sharply and pushes the coefficient towards 1.0.
What is the velocity of approach correction and when does it matter?
It accounts for the fluid in the pipe already moving towards the orifice, so the pressure difference is not converting all of its energy into the jet. The factor is 1 divided by the square root of 1 minus beta to the fourth, where beta is the orifice to pipe diameter ratio. At a beta of 0.4 it is only 1.013, but at a beta of 0.8 it reaches 1.19, so ignoring it would understate the flow by nearly 20 percent on a large meter run.
What diameter ratio should an orifice plate be sized to?
Keep beta between about 0.2 and 0.75. Above 0.75 the permanent pressure loss becomes a large fraction of the measured drop, the coefficient is less well established, and the installation needs long straight runs upstream to keep the profile acceptable. Below 0.2 the coefficient drifts, the plate is sensitive to burrs and to the exact edge condition, and a small hole blocks easily.
Can I use this for a gas or steam orifice?
Only as a first estimate. A gas changes density as it expands across the plate, so the incompressible equation overstates the flow unless an expansion factor is applied, and for steam the condition changes again as it flashes. Use this for liquids, and for gases use the standard with the expansion factor and the upstream density at the tapping.