| Trial | Diameter (mm) | Head (cm) | Volume (L) | Time (s) | Expected Cd (approx.) |
|---|---|---|---|---|---|
| 1 | 10 | 25 | 12.5 | 20 | 0.60–0.70 |
| 2 | 8 | 30 | 9.0 | 18 | 0.58–0.68 |
| 3 | 12 | 20 | 15.0 | 22 | 0.60–0.72 |
- Choose how you measured actual discharge.
- Enter orifice diameter and head with correct units.
- Provide discharge directly or enter volume and time.
- Keep gravity at default unless your lab specifies otherwise.
- Press Calculate to view Cd and intermediate values above.
- Use CSV for spreadsheets or print-friendly PDF for reports.
What the discharge coefficient represents
The discharge coefficient (Cd) describes how real flow through an orifice differs from an ideal prediction. It bundles contraction and velocity effects, so Cd equals actual volumetric flow divided by theoretical flow from area and head. Sharp‑edged plates often fall near 0.60–0.65, while rounded nozzles can approach 0.95. Being dimensionless, Cd helps compare different sizes when conditions are similar.
Theoretical flow basis used in this tool
The calculator uses Qtheoretical = A·√(2gh), where A is orifice area, g is gravitational acceleration, and h is upstream head above the orifice centerline. The relation comes from Bernoulli’s equation with a large reservoir, negligible approach velocity, and no losses. The tool also reports A and Qtheoretical so you can audit inputs and see how head or diameter changes ideal discharge. When using manometers, reference the correct datum and correct for density differences, because small head errors strongly influence theoretical discharge through the square root.
Measuring actual discharge with good practice
Actual flow can be entered directly or computed from collected volume and elapsed time. Use a calibrated tank, or weigh collected mass and convert using density. Start timing only after the jet stabilizes, and run several trials to reduce random error. Report the mean and spread so readers understand repeatability and uncertainty.
Flow regime and installation effects
Cd is not strictly constant: it varies with Reynolds number, edge sharpness, plate thickness, and downstream conditions. Low Reynolds numbers increase viscous losses, lowering Cd. Damaged edges change the vena contracta and create scatter. Provide calm upstream conditions and avoid air entrainment in the measuring tank. If head changes during a run, use an average head or log h versus time for better accuracy.
Interpreting results for design and reporting
Use the computed Cd to predict discharge at other heads for the same geometry, or to validate experimental rigs. In reports, include diameter, head, fluid temperature, and how Qactual was obtained. Compare your value to reference ranges for your orifice type and note test conditions that explain differences. CSV preserves trial data, while PDF export fits lab reports and audits.
What is a typical Cd for a sharp-edged orifice?
Many lab tests for sharp-edged, thin plates report Cd around 0.60 to 0.65 in turbulent water flow. Values outside that range can occur with low Reynolds numbers, thick plates, worn edges, or measurement error.
Why does Cd change with Reynolds number?
At low Reynolds numbers, viscous effects dominate and energy losses rise, reducing Cd. As Reynolds number increases, losses become relatively smaller and Cd approaches a more stable value for a given geometry.
Should I use instantaneous head or average head?
If head is steady, use the measured head. If head drops during collection, use an average head over the timing interval or record head versus time and compute a weighted average for better accuracy.
Can this calculator handle non-water fluids?
Yes, if you measure actual volumetric flow directly. The theoretical term depends on g and head, not density, but fluid properties can affect Cd through Reynolds number. Note the fluid and temperature when reporting results.
What diameter should I enter for a non-circular opening?
Enter the hydraulic equivalent diameter only if you are interpreting Cd for an equivalent area assumption. For strict accuracy, Cd is geometry-specific; use the true area in a custom model and treat results as approximate.
How can I reduce uncertainty in Cd?
Repeat trials, improve timing resolution, calibrate the collection volume, and measure diameter carefully. Keep upstream conditions calm, avoid bubbles, and ensure the jet is fully developed before timing. Small head errors matter, so read head precisely.