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Free orifice formula

Free orifice diagram

Excerpt from CARLIER, M. (1972). Hydraulique générale et appliquée. OCLC : 421635236. Paris : Eyrolles

The general formula for a free orifice or nozzle is as follows (CARLIER, 1972):

\[Q = C_d S \sqrt{2g H}\]


  • \(Q\) the flow in m3/s;
  • \(C_d\) the discharge coefficient;
  • \(S\) the orifice surface in m2;
  • \(g\) the acceleration of gravity 9.81 m/s2
  • \(H\) The water level measured from the surface of the water to the centre of the orifice in meters.

The area \(S\) to be considered is the smallest cross-sectional area of the orifice or nozzle (Figure 5.12c). The discharge coefficient \(C_d\) varies depending on the type of orifice or nozzle. Figure 5.12 shows the most common shapes and discharge coefficients (Source: CARLIER, 1972).