What is the beta ratio?

Beta (β) is the ratio of the orifice bore diameter d to the pipe diameter D. It typically ranges from 0.2 to 0.75. Higher beta means less pressure loss but also less measurement signal.

Why does flow scale with the square root of ΔP?

Bernoulli's equation gives ΔP ∝ V² for incompressible flow. Inverting: V ∝ √ΔP. This means doubling the flow quadruples the differential pressure.

What discharge coefficient should I use?

For a sharp-edged orifice, Cd ≈ 0.61. Machined Venturi tubes achieve Cd ≈ 0.985. Exact values depend on Re and β — standards like ISO 5167 provide detailed correlations.

How is a Pitot tube different from an orifice?

A Pitot tube faces into the flow and measures the stagnation pressure minus static pressure (velocity pressure). It gives point velocity, not average velocity, and causes minimal flow disturbance.

Why do Venturi tubes have higher Cd than orifice plates?

The Venturi's gradual convergence and divergence minimize boundary-layer separation and turbulence, letting the actual flow rate very nearly match the theoretical prediction.

Can I use this for gas flow?

Yes, but for compressible gases at high pressure ratios (ΔP/P > ~10%), apply an expansion factor (ε or Y) to correct for gas density change through the restriction.

Differential Pressure Calculator

Calculate flow rate from differential pressure across orifice plates, Venturi tubes, flow nozzles, and Pitot tubes. Converts ΔP to flow velocity and volume.

Flow device

Fluid

Pipe diameter

Beta ratio (d/D)Orifice bore / pipe diameter

Differential pressure

Unit

Flow Velocity

0.499 m/s

Mean velocity in pipe

Volume Flow (L/s)

3.916

234.9 L/min

Volume Flow (gpm)

62.07

14.10 m³/h

Discharge Coefficient

0.610

Cd — accounts for flow contraction

Beta Ratio

0.500

d = 50.0 mm

Differential Pressure

5.000 kPa

0.725 psi

Flow Rate vs ΔP

0.1

0.25

0.5

ΔP (kPa)

ΔP (kPa)	Q (L/s)	V (m/s)
0.10	0.554	0.071
0.25	0.876	0.111
0.50	1.238	0.158
1.00	1.751	0.223
2.00	2.477	0.315
5.00	3.916	0.499
10.00	5.538	0.705
20.00	7.831	0.997
50.00	12.383	1.577

Planning notes, formulas, and examples

About the Differential Pressure Calculator

Differential pressure (DP) flow measurement exploits Bernoulli's principle: when fluid accelerates through a constriction, its static pressure drops in proportion to the square of its velocity. By measuring the pressure difference across the constriction and knowing the geometry, you can calculate the flow rate precisely.

This calculator supports four primary DP flow devices. The orifice plate is the simplest and most common — a thin plate with a concentric hole. Venturi tubes recover most of the pressure, reducing energy loss. Flow nozzles offer a middle ground, and Pitot tubes measure point velocity directly from velocity pressure ½ρV². Each device has a characteristic discharge coefficient (Cd) that accounts for real-flow effects.

Input your differential pressure in Pa, kPa, psi, inH₂O, or mmHg, and the calculator returns flow velocity, volume flow rate (L/s, L/min, gpm, m³/h), and the discharge coefficient used. The ΔP-vs-flow chart illustrates the square-root relationship between pressure and flow.

When This Page Helps

Differential-pressure flow measurement is used in over 30% of industrial flowmeters worldwide. This calculator helps engineers size orifice plates, check Venturi meters, and convert DP readings to flow rates.

How to Use the Inputs

Select the flow measurement device (orifice plate, Venturi, nozzle, or Pitot tube).
Choose the fluid or enter a custom density.
Enter the pipe diameter and the beta ratio (orifice bore / pipe diameter).
Enter the measured differential pressure and select the unit.
Read the flow velocity and volume flow rate from the outputs.
Use the table to see how flow rate scales with ΔP.

Formula used

Orifice / Venturi / Nozzle:
  Q = Cd × E × A_d × √(2ΔP / ρ)
  E = 1 / √(1 − β⁴), β = d/D

Pitot tube: V = √(2ΔP / ρ)

Where:
• Cd = discharge coefficient
• A_d = orifice area (m²)
• ΔP = differential pressure (Pa)
• ρ = fluid density (kg/m³)

Example Calculation

Result: Q ≈ 0.76 L/s, V ≈ 0.97 m/s

A_d = π/4 × (0.05)² = 1.963×10⁻³ m². E = 1/√(1−0.0625) = 1.033. Q = 0.61 × 1.033 × 0.001963 × √(10000/998) ≈ 0.00393 m³/s ≈ 3.93 L/s — actual numbers vary with precise Cd iterations.

Tips & Best Practices

The permanent pressure loss of an orifice plate is about 60–80% of ΔP; for a Venturi it's only 10–15%.
Always specify upstream and downstream straight-pipe lengths per ISO 5167 for accurate orifice readings.
A square-root extractor is needed in control systems because ΔP ∝ Q².
Temperature changes affect density — always correct ρ for operating conditions.
For a Pitot tube, multiply the centerline velocity by a profile factor (~0.82 turbulent) to get average velocity.

When To Use This Calculator

Calculate flow rate from differential pressure across orifice plates, Venturi tubes, flow nozzles, and Pitot tubes. Converts ΔP to flow velocity and volume. Use it when you need a repeatable calculation in the physics / fluid category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

Beta (β) is the ratio of the orifice bore diameter d to the pipe diameter D. It typically ranges from 0.2 to 0.75. Higher beta means less pressure loss but also less measurement signal.