Coefficient of Discharge Calculator (Cd)
Find the coefficient of discharge for an orifice plate or sharp-edged opening. Enter the orifice diameter, water head, and measured flow rate — the calculator applies Torricelli's theorem to get the theoretical flow rate and computes Cd.
m
m
m³/s
m/s²
Ratio of actual to theoretical flow rate; sharp-edged orifices are typically 0.60–0.65
- 1
Orifice area (A)
π × (0.05 ÷ 2)² = 0.001963 m²Cross-sectional area of the circular orifice. - 2
Theoretical velocity (√2gH)
√(2 × 9.81 × 2) = 6.2642 m/s - 3
Theoretical flow rate (Q_th)
0.001963 × 6.2642 = 0.0123 m³/s - 4
Coefficient of discharge (Cd)
0.0065 ÷ 0.0123 = 0.5285
How does this calculator work?
Cd = Q_actual / Q_theoretical, where Q_theoretical = A × √(2gH) from Torricelli's theorem. For a 50 mm diameter orifice at 2 m head with a measured flow of 0.0065 m³/s, the theoretical flow is about 0.011 m³/s, giving Cd ≈ 0.60. Sharp-edged orifices typically give Cd = 0.60–0.65.
Formula
How this is calculated
Torricelli's theorem states that the theoretical velocity of fluid issuing from a small orifice at the bottom of a large tank is v = √(2gH), where H is the head of fluid above the orifice centreline and g is gravitational acceleration. Multiplying by the orifice area A = π(d/2)² gives the theoretical flow rate Q_th. In reality, viscous friction and the vena contracta (the contraction of the jet just beyond the orifice) mean the actual flow Q_actual is always less.
The coefficient of discharge Cd = Q_actual / Q_th quantifies this real-world efficiency. For a standard sharp-edged circular orifice in a flat plate (an ISO 5167 orifice plate), Cd is typically around 0.60–0.65. Rounded-entrance orifices (nozzles) can reach 0.95–0.99 because they reduce the vena contracta. Cd is usually determined experimentally for a given geometry.
This calculator assumes the orifice is small relative to the tank cross-section (so velocity of approach is negligible) and that the fluid is incompressible with steady flow. For compressible gas flow, an expansion factor Y must also be applied, which is outside the scope of this calculator.
Frequently asked questions
For a sharp-edged circular orifice in a flat plate (ISO 5167 orifice plate), Cd is approximately 0.60–0.65 at high Reynolds numbers. Rounded-entrance nozzles (ISA 1932 or long-radius nozzles) typically achieve 0.95–0.99.
Just downstream of a sharp orifice, the jet continues to contract beyond the orifice diameter due to inertia, reaching its minimum cross-section (the vena contracta) at roughly 0.5–0.6 diameters downstream. The coefficient of contraction Cc = A_vena / A_orifice is typically about 0.64 for a sharp edge.
Flow rate scales with the square root of head: doubling the head increases flow by a factor of √2 ≈ 1.41. This square-root relationship comes from Torricelli's theorem, which derives from Bernoulli's equation applied between the free surface and the orifice.
TG we-Calculate Editorial Team. (2026). Coefficient of Discharge Calculator (Cd) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/coefficient-of-discharge-calculator
TG we-Calculate Editorial Team. "Coefficient of Discharge Calculator (Cd)." TG we-Calculate. 2026. https://we-calculate.com/calculator/coefficient-of-discharge-calculator.
TG we-Calculate Editorial Team, "Coefficient of Discharge Calculator (Cd)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/coefficient-of-discharge-calculator
@misc{wecalculate_coefficient_of_discharge_calculator, title = {Coefficient of Discharge Calculator (Cd)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/coefficient-of-discharge-calculator}}, year = {2026}, note = {TG we-Calculate} }
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