Coefficient of Discharge Calculator

The coefficient of discharge (Cd) is a dimensionless number that represents the ratio of actual flow rate to theoretical flow rate through a device like an orifice, nozzle, or weir. It accounts for real-world energy losses due to friction, turbulence, and vena contracta effects. A perfect, lossless device would have Cd = 1, but in practice values typically range from 0.6 to 0.98 depending on the device type. See also our calculate Lift Coefficient Lift Coefficient (C_L).

The basic formula is Cd = Q_actual / Q_theoretical, where Q_actual is the measured flow rate and Q_theoretical is the ideal flow rate calculated from Torricelli's theorem: Q_th = A × √(2gh). Here A is the orifice area, g is gravitational acceleration, and h is the hydraulic head. Simply divide the actual by the theoretical to get Cd.

For a sharp-edged circular orifice, Cd is typically around 0.61 to 0.65. Rounded entrance nozzles can have Cd values of 0.95 to 0.99, while venturi meters range from 0.95 to 0.98. Broad-crested weirs have values near 0.848, and sharp-crested weirs near 0.611. The exact value depends on the geometry, Reynolds number, and flow conditions.

Theoretical discharge is calculated using the formula Q_theoretical = A × √(2gh), where A is the cross-sectional area of the orifice (m²), g is gravitational acceleration (9.81 m/s²), and h is the hydraulic head above the orifice centre (m). This assumes an ideal, frictionless flow with no energy losses. You might also find our calculate Hydraulic Pressure Push Force (Cap End) useful.

Actual discharge can be calculated from Q_actual = Cd × A × √(2gh), where Cd is the known coefficient of discharge. Alternatively, it can be measured directly using a flow meter, volumetric tank test, or weighing method — dividing the collected volume by the time taken.

The coefficient of discharge is the product of two other coefficients: Cd = Cv × Cc. The coefficient of velocity (Cv) accounts for the reduction in velocity due to friction, typically ranging from 0.97 to 0.99 for sharp-edged orifices. The coefficient of contraction (Cc) accounts for the reduction in jet area due to vena contracta formation, typically around 0.61 to 0.69.

The theoretical flow rate assumes ideal conditions with no energy losses. In reality, viscosity causes friction losses, turbulence dissipates kinetic energy, and the vena contracta (the narrowest point of the jet downstream of an orifice) reduces the effective flow area. These irrecoverable losses mean the actual flow rate is always less than the theoretical value.

Cd is widely used in hydraulic and fluid engineering for designing and calibrating orifice plates, nozzles, venturi meters, weirs, sluice gates, and control valves. Applications include water supply systems, irrigation canals, chemical processing pipelines, dam spillways, and fuel injection systems in engines and aerospace propulsion.