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Orifice Discharge Coefficient and Resistance

Calculate orifice discharge coefficient and resistance with local equations, selectable units and supported inverse relationships.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Area = 0.0078539816; Coefficient of discharge cp = 0.18006326; Flow resistance cp = 30.842514. Values use the worked example unit selections.

Cd = ṁ/[A√(2ρΔp)] or Q/[A√(2gh)]; K = 1/Cd²

Worked example

Enter these known values and leave the other values blank.

Calculate discharge coefficient using...
change in pressure
Fluid
Water scenario (1000 kg/m³)
Diameter (d)
0.1 m
Change in pressure (ΔP)
1000 Pa
Mass flow rate (ṁ)
2 kg/s
Density (ρ)
1000 kg/m³
Area (A)
0.007854 m²
Coefficient of discharge (Cd)
0.18006
Flow resistance (k)
30.84

Assumptions and limitations

  • Steady incompressible orifice flow is assumed. The resistance result is the captured ideal inverse-square definition; it is not a general pipe-network loss coefficient. Material densities are nominal approximations.
  • Unit selectors convert known physical quantities. Leave a supported unknown blank; derived inverse branches are limited by the stated model and available captured equations.
  • The hidden standard-gravity default uses 9.80665 m/s² in metric and a rounded 32.174 ft/s² in customary mode. Reveal gravity to enter a local value.
  • Density presets are explicitly fixed scenarios. Air and oil densities require actual temperature, pressure and composition measurements for application-specific use; these presets are not fluid property correlations.

Common questions

What does this calculation assume?

Steady incompressible orifice flow is assumed. The resistance result is the captured ideal inverse-square definition; it is not a general pipe-network loss coefficient. Material densities are nominal approximations.

Can I solve for an input?

Where the captured model supplies an inverse, leave that quantity blank and enter the remaining known quantities. A positive square-root or principal trigonometric inverse may represent only one of multiple mathematical branches.

Which unit should I use for the worked example?

The example uses the initial metric unit selection beside each field. Change a unit using its selector to convert the same known quantity; switching a unit does not change the underlying physical value.

References

Original accessible explanations preserve the captured diagram geometry, quantities and conditional variants without external image loading. Bookify uses exact customary mass and volume definitions for density units, replacing rounded factors in the reference. Pounds-force per square inch use the exact international pound and inch with standard gravity, replacing the rounded captured factor. Mercury pressure columns use conventional density and standard gravity, with the exact international inch. Volumetric flow rates use exact US or imperial fluid-volume definitions and exact seconds per minute, hour and day. Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor.

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