Coefficient of Discharge
Calculate the coefficient of discharge Cd for fluid flow through an orifice using actual discharge, diameter, and hydraulic head. Free online fluid dynamics calculator with flow resistance, theoretical discharge, and interactive comparison charts for engineers and physics students.
About This Calculator
The Coefficient of Discharge Calculator helps engineers, hydrologists, and physics students determine the discharge coefficient Cd for fluid flow through an orifice, pipe, or weir. The coefficient of discharge is a dimensionless parameter that represents the ratio of actual flow rate to the theoretical flow rate, accounting for energy losses due to friction, turbulence, and contraction in the fluid system.
The calculator uses the standard fluid dynamics formula Cd = Qact / (A × √(2gH)), where Qact is the actual measured discharge, A is the cross-sectional area of the orifice, g is gravitational acceleration, and H is the hydraulic head. The area is automatically computed from the diameter you enter. The flow resistance k = 1/Cd² is also calculated, representing the system's resistance to flow.
Typical Cd values range from 0.60–0.65 for sharp-edged orifices, 0.95–0.99 for venturi meters, and 0.97–0.99 for well-rounded nozzles. The coefficient of discharge is one of three hydraulic coefficients used in fluid mechanics, along with the coefficient of contraction (Cc) and coefficient of velocity (Cv), related by Cd = Cv × Cc.
How to measure the inputs
Diameter: Measure the internal diameter of the orifice or pipe opening in millimeters. For non-circular openings, compute the equivalent diameter from the cross-sectional area.
Head: The hydraulic head is the height of the fluid surface above the center of the orifice, measured in meters. This represents the potential energy driving the flow.
Actual discharge: Collect the fluid flowing through the orifice in a container of known volume. Divide the volume (in m³) by the collection time (in seconds) to obtain the actual discharge in m³/s.
Regional Notes
Worldwide: This calculator uses SI units (metric system) universally — millimeters, meters, m³/s, and m/s². The gravitational acceleration default of 9.80665 m/s² is suitable for most locations on Earth. Users in regions using imperial units should convert inches to mm (1 in = 25.4 mm) and feet to meters (1 ft = 0.3048 m) before entering values.
Frequently Asked Questions
What is the coefficient of discharge?
The coefficient of discharge (Cd) is the ratio of actual discharge to theoretical discharge for a fluid flow through an orifice, venturi, or weir. It accounts for irrecoverable losses in the system and typically ranges from 0.6 to 0.65 for sharp-edged orifices.
How do you calculate the coefficient of discharge?
The coefficient of discharge is calculated as Cd = Q_act / (A × √(2gH)), where Q_act is the actual discharge in m³/s, A is the cross-sectional area in m², g is gravitational acceleration (9.80665 m/s²), and H is the hydraulic head in meters.
What is a typical coefficient of discharge value?
For a sharp-edged orifice, the coefficient of discharge typically ranges from 0.60 to 0.65. For venturi meters, Cd is around 0.95 to 0.99. For a well-rounded orifice, Cd can approach 0.98. The value depends on the geometry and flow conditions.
What is the relationship between Cd, Cv, and Cc?
The coefficient of discharge (Cd) is related to the coefficient of velocity (Cv) and coefficient of contraction (Cc) by the equation Cd = Cv × Cc. Cv relates to the velocity of the fluid jet, while Cc accounts for the reduction in cross-sectional area of the jet after the orifice.
How do I measure actual discharge for flow through an orifice?
To measure actual discharge, collect the fluid in a container of known volume and measure the time required to fill it using a stopwatch. The actual discharge Q_act is then calculated as the collected volume divided by the collection time.
What is flow resistance k and how is it related to Cd?
Flow resistance k is a dimensionless parameter that represents the resistance offered by the surroundings to fluid flow. It is directly related to the coefficient of discharge by the formula k = 1/Cd². A lower Cd corresponds to higher flow resistance.
What are the three hydraulic coefficients in fluid mechanics?
The three hydraulic coefficients are: (1) Coefficient of discharge (Cd) which relates actual to theoretical flow rate, (2) Coefficient of contraction (Cc) which relates the jet area to the orifice area, and (3) Coefficient of velocity (Cv) which relates actual to theoretical velocity of the fluid jet.
What units should I use for the coefficient of discharge calculator?
This calculator uses millimeters for diameter, meters for hydraulic head, m³/s for actual discharge, and m/s² for gravitational acceleration. The gravitational acceleration default is 9.80665 m/s² but can be adjusted for different locations or planetary bodies.