🚰 Coefficient of Discharge Calculator
Enter the actual measured flow rate, orifice area, and pressure head to calculate the coefficient of discharge (Cd) for an orifice or nozzle.
What is coefficient of discharge?
The coefficient of discharge (Cd) compares the actual flow rate through an orifice, nozzle, or weir to the theoretical flow rate predicted by ideal fluid dynamics, capturing real-world losses from friction, turbulence, and flow contraction (the vena contracta).
The formula
Theoretical velocity through an orifice under a head H is found from Torricelli’s law: v = √(2gH). Multiplying by orifice area gives theoretical flow, Qtheoretical = A × v. The coefficient of discharge is then Cd = Qactual ÷ Qtheoretical, typically between 0.6 and 0.98 depending on orifice geometry.
Cd values vary significantly with orifice edge shape (sharp-edged vs. rounded), Reynolds number, and installation, so measured or manufacturer-supplied values are more reliable than assumed constants for engineering design. This calculator is for general fluid mechanics education.