Coefficient of Discharge Calculator
Calculate the discharge coefficient for fluid flow through orifices, weirs, and other hydraulic devices
Calculate Coefficient of Discharge
Geometry Parameters
For circular cross-sections (pipes, orifices)
Automatically calculated from diameter
Height of fluid above the orifice center
Measured volumetric flow rate
Results
Formula used: Cd = Q_actual / Q_theoretical
Theoretical discharge: Q_th = A × √(2gH) or Q_th = A × √(2ΔP/ρ)
Flow resistance: k = 1/Cd²
Coefficient Analysis
Example Calculation
Orifice Flow Example
Problem: Water flows through a 40 mm diameter orifice
Hydraulic head (H): 10 m
Measured discharge: 0.01056 m³/s
Diameter (d): 0.04 m
Solution
Area = π × (0.04/2)² = 0.001257 m²
Q_theoretical = 0.001257 × √(2 × 9.8066 × 10) = 0.0176 m³/s
Cd = 0.01056 / 0.0176 = 0.6
k = 1/(0.6)² = 2.78
Hydraulic Coefficients
Coefficient of Discharge
Ratio of actual to theoretical flow rate
Typical range: 0.6 - 0.65
Coefficient of Contraction
Ratio of jet area to orifice area
Typical range: 0.61 - 0.64
Coefficient of Velocity
Ratio of actual to theoretical velocity
Cd = Cv × Cc
Measurement Tips
Measure head from free surface to orifice centerline
Ensure steady flow conditions for accurate results
Account for temperature effects on fluid density
Use multiple measurements to improve accuracy
Understanding Coefficient of Discharge
What is Coefficient of Discharge?
The coefficient of discharge (Cd) is a dimensionless parameter that represents the ratio between actual and theoretical discharge in fluid flow through restrictions like orifices, weirs, or venturi meters. It accounts for energy losses due to friction, turbulence, and flow contraction.
Why is it Important?
- •Compensates for real-world flow losses and inefficiencies
- •Essential for accurate flow measurement and design
- •Helps predict actual performance of hydraulic systems
- •Used in calibrating flow measurement devices
Formula Explanation
Cd = Q_actual / Q_theoretical
Q_theoretical = A × √(2gH)
- Cd: Coefficient of discharge (dimensionless)
- Q_actual: Measured discharge rate (m³/s)
- Q_theoretical: Ideal discharge rate (m³/s)
- A: Cross-sectional area (m²)
- g: Gravitational acceleration (9.8066 m/s²)
- H: Hydraulic head (m)
Note: For pressure-based calculations, use Q_th = A × √(2ΔP/ρ)
Applications
Orifice Plates
Flow measurement in pipelines, Cd ≈ 0.6-0.65
Weirs
Open channel flow measurement, Cd varies with design
Venturi Meters
High accuracy flow measurement, Cd ≈ 0.95-0.99