Differential Flowmeter
Compute volumetric flow rate and velocity for orifice/Venturi/Pitot differential-pressure flowmeters from Bernoulli's equation.
Inputs
Formula
A = πd²/4; Q = Cd·A·√(2Δp/ρ); v = Q/A
Fundamentals
A flow meter measures pipe flow; differential-pressure types infer flow from the pressure drop across a restriction.
DP flow $Q=C_d A_2\sqrt{2\Delta p/\rho}$, $C_d$ discharge coeff, $\rho$ density, $\Delta p$ pressure drop. The throat speeds up and pressure drops.
History
Differential-pressure flow meters rest on Bernoulli (1738) and Venturi (1797) and were industrialised in the 20th c.
Engineering applications
Used for flow metering and process control in water, oil and chemical lines.
Glossary
| Flow $Q$ | Volume passing per unit time. |
| Pressure drop $\Delta p$ | Differential across the restriction. |
| Discharge $C_d$ | Correction for real vs ideal flow. |
How to use
- Fill in Orifice dia. d, Pressure diff. Δp, Fluid density ρ, Discharge coeff. Cd in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Vol. flow Q, Velocity v in the results area.
Formula notesOrifice/nozzle flow Q = C_d·A₂·√(2·Δp/ρ); C_d discharge coeff, Δp pressure drop, ρ density.
Formula · Worked Example · Knowledge
Formula
Differential flowmeter: $A=\pi d^2/4$, $Q=C_d A\sqrt{2\Delta p/\rho}$, $v=Q/A$ (Bernoulli).
Worked Example
d=50 mm, Δp=10 kPa, ρ=1000, Cd=0.61 → Q≈0.0107 m³/s, v≈5.4 m/s.
Key Points
- C_d depends on element shape and Reynolds number.
- Pressure loss grows with flow squared.
- Orifice plates are simple but lose more permanent head.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Orifice dia. d (mm) | d | mm | 50 |
| Pressure diff. Δp (kPa) | dp | kPa | 10 |
| Fluid density ρ (kg/m³) | rho | kg/m³ | 1000 |
| Discharge coeff. Cd | Cd | 0.61 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Vol. flow Q | Q | m³/s |
| Velocity v | v | m/s |
Applications
- Pipe flow rate and pressure drop
- Hydraulic cylinder force/speed design
- Flow-meter selection and calibration
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: A = πd²/4; Q = Cd·A·√(2Δp/ρ); v = Q/A
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Pipe flow rate and pressure drop