Calculate the pressure drop across an orifice plate from pipe and bore diameters and flow, using typical water density and Cd, or solve for flow from ΔP.
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Orifice Pressure Drop Formula
This calculator estimates the differential pressure between specified taps around an orifice plate in a liquid-filled pipe. Static pressure partly recovers downstream, so this differential is not the permanent pressure loss. The supplied Cd must match the geometry, taps and flow regime.
The most direct definition of pressure drop is the difference between upstream and downstream pressure:
ΔP = upstream tap pressure − downstream tap pressure
For the incompressible in-pipe model used here, β = bore diameter / pipe inside diameter, with0 < β <1:
Q = Cd × A × √[2ΔP / (ρ × (1 − β⁴))]
Rearranging the equation to solve for pressure drop gives:
ΔP = (ρ/2) × [Q/(Cd × A)]² × (1 − β⁴)
If you know fluid velocity instead of volumetric flow rate, use the flow conversion below:
Q = A × V, where V = nominal Q/A
Substituting velocity into the pressure-drop form gives:
ΔP = ρ × V² × (1 − β⁴) / (2 × Cd²)
In practical use, this means pressure drop increases with fluid density and rises rapidly as velocity increases. If flow rate stays the same, a smaller orifice area forces velocity upward, which increases the differential pressure.
Variable Definitions
| Variable | Meaning | Common Units |
|---|---|---|
| ΔP | Pressure drop across the orifice | Pa, kPa, bar, psi |
| P1 | Upstream pressure | Pa, kPa, bar, psi |
| P2 | Downstream pressure | Pa, kPa, bar, psi |
| C or Cd | Discharge coefficient used to account for contraction and real-flow losses | Dimensionless |
| ρ | Fluid density | kg/m3, lb/ft3 |
| A | Cross-sectional area of the orifice opening | m2, ft2, in2 |
| V | Nominal flow divided by bore area, not contracted-jet velocity | m/s, ft/s |
| Q | Volumetric flow rate | m3/s, ft3/s |
How to Use the Calculator
- Choose differential pressure from flow, or flow from differential pressure. Pick the liquid, or choose Custom density and enter it in kg/m³.
- Keep the typical discharge coefficient of 0.61, or enter the one for your orifice geometry.
- Enter pipe inside diameter and the smaller circular bore diameter. Select the unit beside each input; area and beta are calculated internally.
- Enter the known flow or differential pressure in its selected unit. You do not need to convert it to velocity first.
- Calculate the missing value and confirm the result is in the expected pressure unit.
For a circular orifice, area is found from diameter with:
A = πd²/4
If your known value is flow rate rather than velocity, convert first with:
nominal V = Q/A
What Changes the Pressure Drop?
- Velocity: Pressure drop scales with the square of velocity, so even a modest increase in speed can produce a much larger differential pressure.
- Density: Denser fluids create a larger pressure drop at the same velocity.
- Orifice size: For the same flow rate, a smaller opening increases velocity and therefore increases pressure drop.
- Discharge coefficient: At fixed geometry and flow, a lower specified Cd requires a greater tap differential. Cd must match the actual plate, taps and flow regime.
- Flow regime and geometry: Edge shape, plate thickness, Reynolds number, and installation details can all affect the result.
Example
Suppose density is1000 kg/m3, bore area is2.0 ×10−4 m2 (circular diameter approximately15.957691 mm), flow is0.0012 m3/s, Cd is0.62, and β is0.5 (pipe inside diameter approximately31.915382 mm).
V =0.0012 /0.0002 =6 m/s
ΔP =1000 ×6² ×(1 −0.5⁴) /(2 ×0.62²) ≈43,899.584 Pa
Including the pipe approach factor1 − β⁴ =0.9375, the estimated tap differential is about43.9 kPa. The46.8 kPa value without this factor is the β→0 approximation, not this finite-pipe example.
Important Assumptions
- The calculation assumes steady flow through the restriction.
- It is most useful when density does not change significantly across the orifice.
- The discharge coefficient should match the actual orifice geometry as closely as possible.
- Measured upstream and downstream pressures should be taken at consistent locations.
- Detailed design for gases or high-accuracy metering may require additional corrections for compressibility, expansibility, and installation effects.
Common Questions
Why does pressure drop increase so quickly?
Because velocity is squared in the governing relationship. Doubling velocity can increase pressure drop by roughly a factor of four.
Do I need area if I already know velocity?
The calculator requires both pipe and bore diameter and uses flow or differential pressure directly. Q/A is reported as a nominal bore-area velocity; it is not necessarily the contracted jet velocity.
Can this calculator be used for gases?
This calculator is for incompressible liquids. Gas metering requires appropriate compressibility, expansibility and operating-condition treatment; this output does not establish gas-flow accuracy.
