Orifice Flow Calculator
Discharge through a sharp-edged orifice
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Need a fast answer on discharge through a sharp-edged orifice? Orifice Flow Calculator answers with the steps beside it. Drop Discharge Coefficient Cd, Orifice Diameter (m) and Head Above Orifice (m) into Orifice Flow — the figure refreshes as you type. In Orifice Flow the working sits beside the answer. Use Orifice Flow for a reliable number, fast. Nothing typed into Orifice Flow leaves your device or the tab. Orifice Flow handles orifice flow calculator discharge coefficient tank drainage torricelli the same way as free online orifice flow calculator — one of the Engineering tools on CalcProMaster. Orifice Flow is designed for real people. Labels stay plain. No sign-up or email — Orifice Flow answers as you type.
What the defaults give
A 50 mm orifice with Cd 0.62 under 2 m of head flows at 7.63 L/s.
The theoretical jet velocity is 6.26 m/s; the coefficient accounts for the contraction of the jet and the friction through the opening.
The formula
Q = Cd × A × √(2gh)
A = πd²/4 = π × 0.05² ÷ 4 = 0.0019635 m²
√(2 × 9.81 × 2) = 6.264 m/s
Q = 0.62 × 0.0019635 × 6.264 = 0.00763 m³/s = 7.63 L/s.
Worked examples
50 mm, Cd 0.62, 2 m head → 7.63 L/s
50 mm, Cd 0.62, 8 m head → 15.26 L/s (double the head, not double the flow)
25 mm, Cd 0.62, 2 m head → 1.91 L/s (a quarter of the area)
100 mm, Cd 0.62, 2 m head → 30.5 L/s
Why flow scales with the square root of head
Velocity rises with the square root of the head, so quadrupling the head only doubles the velocity and the flow. Area, by contrast, scales linearly — doubling the diameter quadruples the discharge. If more flow is needed, a larger opening is usually more effective than a taller tank.
Choosing Cd
- Sharp-edged orifice: 0.60–0.62, the standard case.
- Well-rounded inlet: 0.95–0.98, with almost no contraction.
- Short tube or nozzle: 0.80–0.85 depending on length and finish.
- Long pipe outlet: friction dominates and this equation no longer applies.
The equation assumes a free discharge into air, a steady water level and a head measured from the centre of the orifice to the surface. A tank emptying, a submerged outlet or a pipe connection each change the problem and need a different model.
The discharge coefficient is where the accuracy lives. A sharp-edged orifice runs about 0.62, a rounded entry closer to 0.98, and the difference is a third of the flow for the same hole and head. The Torricelli velocity of 6.26 m/s is the ideal, and the coefficient scales it to the real 7.63 L/s through a 5 cm opening under 2 m of head. Viscosity and the approach pipe matter most at low heads.
Frequently Asked Questions
How much water flows through a 50 mm hole?
About 7.63 litres a second under 2 m of head with a sharp-edged coefficient of 0.62.
What is the discharge coefficient?
A correction for the vena contracta and friction, typically 0.60–0.62 for a sharp-edged orifice and about 0.97 for a well-rounded inlet.
Why does doubling the head not double the flow?
Because velocity rises with the square root of head. Four times the head doubles the velocity; area is what scales linearly.
Does the orifice shape matter?
Yes. A rounded inlet flows up to 60% more than a sharp edge because the jet does not contract as much.
Can I use this for a pipe outlet?
Only for a very short one. Once pipe friction dominates, use the Darcy-Weisbach or Hazen-Williams equations instead.
What head should I enter?
The vertical distance from the water surface to the centre of the orifice. For a submerged outlet, use the difference in level between the two surfaces.
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