Free · Fluid mechanics
Orifice Discharge from Area and Head
Estimate steady liquid discharge using opening area, centerline head, gravity and an empirical discharge coefficient.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
With area 100 mm², head 1 m, gravity 2 m/s² and Cd 0.5, the model gives 0.0001 m³/s (0.1 L/s).
Q = Cd A sqrt(2 g H); A = pi d² / 4
Worked example
Enter these known values and leave the other values blank.
- Area of orifice (A)
- 100 mm²
- Centerline head (H)
- 1000 mm
- Gravitational acceleration (g)
- 2 m/s²
- Coefficient of discharge (Cd)
- 0.5
- Diameter of orifice (d)
- 11.284 mm
- Discharge (Q)
- 0.0001 m³/s
Assumptions and limitations
- Steady incompressible liquid flow from a large reservoir to an outlet at the same external pressure. Head is measured vertically from the liquid surface to the opening center.
- The empirical discharge coefficient represents contraction and losses. Select a coefficient justified for the actual opening; this calculation does not determine it. This same-pressure model bounds Cd at1, the ideal lossless discharge.
- The circular diameter relationship assumes a round opening. Enter area directly when the opening shape differs. This model does not account for changing tank level, pressurized upstream flow, cavitation or compressible gas.
- Gravity is editable and defaults to the captured local approximation. Set the physical acceleration explicitly when comparing different unit preferences.
Common questions
Can I calculate discharge from area instead of diameter?
Yes. Area enters the discharge equation directly. The diameter control is the equivalent circular diameter for that area.
What does discharge coefficient mean?
It multiplies ideal Torricelli discharge to represent real flow losses and contraction; its value depends on opening geometry and operating conditions.
References
For steady discharge from a large same-pressure reservoir with losses, the discharge coefficient cannot exceed the ideal Torricelli discharge: require 0 < Cd <= 1.