Case 1
- Discharge coefficient Cd
- 0.62
- Orifice area A
- 0.01m²
- Head above the orifice h
- 2m
- Gravitational acceleration g
- 9.81m/s²
0.038838m³/s
Open with these valuesOrifice Flow Rate Calculator
0.038838m³/s
Result: 0.038838 m³/sQ = Cd × A × √(2gh): the ideal jet speed times the hole area, scaled down by the discharge coefficient. Use Cd ≈ 0.62 for a sharp-edged orifice and 0.97 for a rounded nozzle — that factor is measured, not derived, and it depends on the shape of the opening.
Worked examples
Case 2
- Discharge coefficient Cd
- 0.6
- Orifice area A
- 0.05m²
- Head above the orifice h
- 5m
- Gravitational acceleration g
- 9.81m/s²
0.297136m³/s
Open with these valuesCase 3
- Discharge coefficient Cd
- 0.61
- Orifice area A
- 0.005m²
- Head above the orifice h
- 3m
- Gravitational acceleration g
- 9.81m/s²
0.023400m³/s
Open with these valuesHow it's calculated
Q = Cd × A × √(2 × g × h)
- StepPick the discharge coefficient: 0.62 for a sharp hole, 0.97 for a rounded nozzle.
- StepEnter the area of the opening and the fluid height above it.
- StepLeave gravity at 9.81 m/s² unless you need another planet.
- ResultRead the flow in cubic metres per second at that head.
Reference table
| Cd, A, h, g | Opening | Q (m³/s) |
|---|---|---|
| 0.62, 0.01, 2, 9.81 | Sharp-edged | 0.038838 |
| 0.62, 0.01, 1, 9.81 | Sharp-edged, half the head | 0.027463 |
| 0.6, 0.05, 5, 9.81 | Large sharp hole | 0.297136 |
| 1, 0.01, 2, 9.81 | Ideal, no contraction | 0.062642 |
| 0.61, 0.005, 3, 9.81 | Small sharp hole | 0.023400 |
Questions
How do I calculate the flow rate through an orifice?
Use Q = Cd × A × √(2 × g × h): the discharge coefficient times the opening area times the ideal jet speed. With Cd 0.62, A 0.01 m², h 2 m and g 9.81 m/s² the jet leaves at 6.264 m/s and Q is about 0.038838 m³/s.
What value should I use for the discharge coefficient?
It is a dimensionless factor between 0 and 1 that scales the ideal flow to the real flow. A sharp-edged orifice sits near 0.62, a well-rounded nozzle reaches 0.97 or more. Pick the value that matches the shape of your opening.
What is the vena contracta?
Just past a sharp orifice the streamlines keep converging, so the jet narrows to a cross-section smaller than the hole. Because the effective flow area is smaller than the opening, the real discharge stays below the ideal A × v — that gap is what the discharge coefficient carries.
Does the fluid density change the result?
The exit speed √(2gh) does not depend on density, so water and oil leave the same head at the same ideal speed. Density matters for the mass per second and for the discharge coefficient at very low Reynolds numbers, but not for the volume flow itself.
Does the flow stay constant while the tank drains?
No. As the head h drops, the speed √(2gh) falls with it and the flow tapers off. This calculator gives the instantaneous flow at the head you enter, not an average over the emptying.
Sources and last check
Information, not professional advice.