Free orifice formula

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):

$$Q=C_{d}S\sqrt{2gH}$$

With:

• $Q$ 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).