Orifice Flow Calculator — Discharge Through an Orifice
Enter the orifice diameter, the pressure head above it and the discharge coefficient, and the calculator returns the volumetric flow rate in L/s, m³/s and m³/h, plus the jet velocity through the opening.
mm
m
Flow through the orifice under the given head
- 1
Orifice area A = π × (d/2)²
π × (50 mm ÷ 2 ÷ 1000)² = 0.001963 - 2
2 × g × h
2 × 9.807 × 3 = 58.8399 - 3
Jet velocity = √(2gh)
√58.8399 = 7.6707 - 4
Q = Cd × A × √(2gh) in L/s
0.61 × 0.001963 × 7.6707 × 1000 = 9.1875
How does this calculator work?
Flow rate through an orifice is Q = Cd × A × √(2gh), where Cd ≈ 0.61 for a sharp-edged hole, A is the orifice area, g = 9.807 m/s², and h is the pressure head in metres. Enter diameter, head and Cd to get flow in L/s, m³/s, and m³/h.
Formula
How this is calculated
When fluid sits above a sharp-edged opening, the pressure difference drives a jet through the orifice. The theoretical velocity at the vena contracta (the jet's narrowest point) follows Torricelli's theorem: v = √(2gh). The actual volumetric flow is less than the theoretical value because (a) the flow contracts to a cross-section smaller than the orifice area, and (b) friction losses reduce velocity. Both effects are lumped into the dimensionless discharge coefficient Cd = actual flow / theoretical flow.
For a standard sharp-edged circular orifice in a thin plate, Cd ≈ 0.61 at high Reynolds numbers. Rounded nozzles achieve Cd ≈ 0.97–0.99 by eliminating the vena contracta. Values for other geometries (square-edged, partially submerged, valve openings) should come from calibration data or published tables — the default 0.61 is a conservative starting point for water.
The formula assumes incompressible, steady-state flow, negligible approach velocity (large reservoir), and that the orifice discharges freely into air. The Q-versus-head curve displayed scales with √h, so doubling the head raises the flow by about 41%, not 100%.
Frequently asked questions
Cd is the ratio of actual flow through the orifice to the theoretically ideal flow. It accounts for jet contraction at the vena contracta (coefficient of contraction, Cc ≈ 0.64) and velocity losses (Cv ≈ 0.97). For a sharp-edged orifice Cd = Cc × Cv ≈ 0.61; rounded nozzles can reach 0.97–0.99.
Yes — Cd varies with Reynolds number and orifice geometry. At low Reynolds numbers (viscous flow) Cd can drop significantly. The value 0.61 applies to fully turbulent flow through a sharp-edged orifice in a large reservoir; for accurate results, use calibration data specific to your fitting.
Head must be entered in metres (the height of the liquid surface above the orifice centreline). The calculator uses g = 9.807 m/s². If your head is in other units, convert first: 1 ft ≈ 0.305 m, 1 in ≈ 0.0254 m.
Also known as
TG we-Calculate Editorial Team. (2026). Orifice Flow Calculator — Discharge Through an Orifice [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/orifice-flow-calculator
TG we-Calculate Editorial Team. "Orifice Flow Calculator — Discharge Through an Orifice." TG we-Calculate. 2026. https://we-calculate.com/calculator/orifice-flow-calculator.
TG we-Calculate Editorial Team, "Orifice Flow Calculator — Discharge Through an Orifice," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/orifice-flow-calculator
@misc{wecalculate_orifice_flow_calculator, title = {Orifice Flow Calculator — Discharge Through an Orifice}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/orifice-flow-calculator}}, year = {2026}, note = {TG we-Calculate} }
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