Orifice Flow Calculator
Discharge through an orifice from upstream head and orifice area. The classical Torricelli formula plus a discharge coefficient for the contracted jet.
Defaults: 6-inch round sharp-edged orifice, 4 ft of water head, Cd = 0.61.
Discharge coefficient values
- Sharp-edged orifice (thin plate): Cd = 0.60 to 0.62
- Rounded entrance (well-shaped): Cd = 0.95 to 0.98
- Short tube (Borda mouthpiece, length ≈ 2–3 D): Cd ≈ 0.51
- Re-entrant tube (Borda's mouthpiece): Cd ≈ 0.51
- Standard short tube: Cd ≈ 0.82
The discharge coefficient combines the contraction coefficient (jet shrinks below the orifice area, called the vena contracta) and the velocity coefficient (real velocity less than ideal due to friction). For most engineering work with sharp-edged orifices, Cd = 0.61 is the standard.
Free vs. submerged orifice
For a free orifice (jet discharges into atmosphere), H is measured from the water surface upstream to the orifice centroid. For a submerged orifice (downstream water level above the orifice), H is the difference in water surface elevations on either side of the orifice. The discharge equation is the same; the head definition changes.
Where this calculator applies
This is the standard equation for: gate openings on small dams, drop inlets and sluice gates, orifice plate flow meters in pipes, low-flow outlet works for stormwater detention basins, valve-gallery openings, and tank drainage time problems. For very large gates where velocity head upstream is non-negligible (drawdown over 10% of total head), use the more general energy equation rather than this simplified form.
Tank drainage time
If you're computing the time to drain a tank through an orifice, you can integrate dV/dt = −Q over the head range. For a constant-cross-section tank: t = 2Atank · (√H₁ − √H₂) / (Cd·A·√(2g)). That's a separate but related calculation.
Reference: Brater, E.F., King, H.W., Lindell, J.E., Wei, C.Y. (1996). Handbook of Hydraulics (7th ed.), Chapter 4. Original: Torricelli's law (1643).