Coefficient of Discharge Calculator
The coefficient of discharge calculator helps you determine the ratio between the theoretical and actual discharge (flow rate) values for a fluid flow. Whether it is the water supply to your house, gas pipelines, or water in an artificial canal, the estimated or theoretical fluid flow used to design these systems is always higher than the actual flow rate for fluids.
The difference comes from a hydraulic system's irrecoverable losses. Therefore, a parameter — the discharge coefficient — is introduced into the calculations to account for the reduction in the flow rate. It is a function of area, flow rate, and head or pressure drop. Read on to understand how to calculate the coefficient of discharge.
What is discharge coefficient?
In simple terms, the discharge coefficient is the ratio of the actual flow rate to the theoretical flow rate. The coefficient of discharge is a dimensionless parameter. It is one of the three hydraulic coefficients:
- Coefficient of discharge, Cd — relates actual and theoretical discharge;
- Coefficient of contraction, Cc — relates the area of the jet to the area of the orifice; and
- Coefficient of velocity, Cv — relates the actual and theoretical velocities of a fluid jet.
The three hydraulic coefficients are related to each other:
Cd = Cv × Cc
Discharge coefficient — orifice, venturi, weir, open channel flows and others
Consider a fluid flow with a constant cross-sectional area. The coefficient of discharge Cd is:
Cd = Qact / Qth
where Qact is the actual discharge (measured at one end of the orifice, sometimes written as ṁ) and Qth is the theoretical discharge given by:
Qth = ρAc = A√(2ρΔP) ... = A√(2gH)
where:
- ρ — density of the fluid;
- A — area of cross-section;
- c — flow velocity;
- ΔP — change in pressure (pressure drop);
- g — acceleration due to gravity; and
- H — head of fluid, i.e., the height or elevation of the top surface of the liquid.
The same idea applies to orifices, venturi meters, weirs, nozzles and open channel flows — only the way the theoretical discharge is computed changes. Typical discharge coefficients are about 0.6–0.65 for a sharp-edged orifice, 0.95–0.99 for a well-designed venturi meter, and 0.6–0.65 for a sharp-crested weir.
How to calculate coefficient of discharge
- Choose your unit system — metric (SI) or American (imperial).
- Select the calculation method: from head/height (H) or from pressure drop (ΔP).
- Enter the actual discharge Qact measured for the system.
- Enter the cross-sectional area A of the opening.
- Enter the head H (for the head method) or the pressure drop ΔP and fluid density ρ (for the pressure method).
- The calculator computes the theoretical discharge Qth and then Cd = Qact / Qth.
Example: Using the coefficient of discharge calculator
Suppose water flows through an orifice with a cross-sectional area of 0.01 m² under a head of 2 m, and the measured actual discharge is 0.05 m³/s.
- Theoretical discharge: Qth = A√(2gH) = 0.01 × √(2 × 9.80665 × 2) ≈ 0.0626 m³/s
- Coefficient of discharge: Cd = 0.05 / 0.0626 ≈ 0.80
A value of Cd close to 0.8 indicates moderate energy losses — higher than a sharp orifice but lower than a smooth venturi.
FAQs
What is a typical discharge coefficient?
For a sharp-edged orifice the discharge coefficient is usually about 0.6–0.65. A venturi meter is much more efficient, with Cd values from 0.95 up to 0.99. Sharp-crested weirs are typically around 0.6–0.65.
Can the discharge coefficient be greater than 1?
No. Because real losses always make the actual discharge smaller than the theoretical discharge, Cd should be less than or equal to 1. A value above 1 usually means an input error (for example, the wrong area, head, or pressure drop).
Is the discharge coefficient dimensionless?
Yes. The discharge coefficient is the ratio of two flow rates with the same units, so it has no units. The same Cd value is obtained whether you work in metric or American units.
What is the difference between Cd, Cv and Cc?
The coefficient of discharge Cd deals with flow rate, the coefficient of contraction Cc with the change in cross-sectional area of the jet, and the coefficient of velocity Cv with the actual versus theoretical velocity. They are linked by Cd = Cv × Cc.