Fluid Mechanics

Venturi Calculator

Calculate Venturi flow rate, pressure drop, throat diameter, discharge coefficient, beta ratio, velocities, and mass flow for incompressible liquid flow.

Formula Q = Cd A2 sqrt(2 Delta p / (rho (1 - beta^4)))Reviewed Sep 2, 2026

A Venturi meter estimates flow from the pressure difference between an upstream pipe section and a smaller throat. This Venturi calculator uses the incompressible relationship Q = Cd A2 sqrt(2 Delta p / [rho(1 - beta^4)]), where beta = d2 / d1. It also reports beta ratio, inlet and throat velocity, velocity increase, and mass flow so the result is more actionable than a bare flow number.

Calculation Bench

Solve for

01Inlet Diameter

d1 · Upstream pipe diameter at pressure tap

02Throat Diameter

d2 · Smaller throat diameter

03Differential Pressure

Δp · Pressure drop from inlet tap to throat tap

04Fluid Density

rho · Use 1000 kg/m³ for water near room temperature

05Discharge Coefficient

Cd · 0.98 is a clean Venturi starting point

Use differential pressure from inlet tap to throat tap. For gases, steam, or cavitation risk, use a more complete meter model.

Solution

Enter Venturi geometry, density, Cd, and pressure or flow to calculate the missing value.

Q = Cd A2 √(2Δp/(ρ(1-β⁴)))

Formula Sheet

Q=C_dA_2\sqrt{\dfrac{2\Delta p}{\rho(1-\beta^4)}}

\Delta p=\dfrac{\rho}{2}\left(\dfrac{Q}{C_dA_2}\right)^2(1-\beta^4)

\beta=\dfrac{d_2}{d_1}

A_2=\dfrac{\pi d_2^2}{4}

v=\dfrac{Q}{A}

\dot{m}=\rho Q

QFlow Rate
CdDischarge Coefficient
d1Inlet Diameter
d2Throat Diameter
A1Inlet Area
A2Throat Area
betaBeta Ratio
Delta pDifferential Pressure
rhoFluid Density
v1Inlet Velocity
v2Throat Velocity
m_dotMass Flow Rate

Venturi Quick Checks

Check	Screening range	Meaning
Beta ratio	0.30 to 0.75 typical	Very low beta increases velocity; high beta reduces DP sensitivity
Clean Venturi Cd	about 0.98	Use calibrated/manufacturer Cd for real metering accuracy
Throat velocity	1 to 5 m/s typical	Higher values need noise, erosion, and cavitation review
Model scope	liquids only	Gas/steam needs compressibility and expansion-factor checks

Variables & Units

Symbol	Variable	Description	Common Units
Q	Flow Rate	Volumetric flow through the Venturi.	L/s, m³/h, US gpm
Cd	Discharge Coefficient	Empirical correction from ideal to actual Venturi flow.
d1	Inlet Diameter	Upstream pipe diameter at the pressure tap.	mm, in
d2	Throat Diameter	Smaller Venturi throat diameter.	mm, in
A1	Inlet Area	Cross-sectional area at the inlet.	m², in²
A2	Throat Area	Cross-sectional area at the throat.	m², in²
beta	Beta Ratio	Throat diameter divided by inlet diameter.
Delta p	Differential Pressure	Pressure difference between inlet and throat taps.	kPa, psi, bar
rho	Fluid Density	Liquid mass density.	kg/m³, lb/ft³
v1	Inlet Velocity	Average velocity in the inlet section.	m/s, ft/s
v2	Throat Velocity	Average velocity in the throat.	m/s, ft/s
m_dot	Mass Flow Rate	Mass flow, equal to density times volumetric flow.	kg/s

How to Use This Calculator

01Choose what you want to solve for: flow rate, pressure drop, throat diameter, or discharge coefficient.
02Enter inlet diameter d1 and throat diameter d2. The throat must be smaller than the inlet.
03Use the differential pressure between the upstream tap and throat tap, not the absolute line pressure.
04Enter liquid density and a discharge coefficient. A well-formed Venturi often uses a Cd close to 0.98, but real values depend on geometry and Reynolds number.
05Review beta ratio and throat velocity. Very high beta ratios are less sensitive; very high throat velocity can indicate noise, erosion, cavitation, or installation issues.

How the Formula Works

Continuity says the same flow passes through the inlet and throat, so velocity increases at the smaller throat area. Bernoulli's equation links that velocity increase to a pressure drop.

The beta-ratio correction 1 - beta^4 is what separates a Venturi meter from a simple free-orifice equation. It accounts for velocity of approach in the upstream pipe.

The discharge coefficient Cd corrects ideal Venturi flow for real losses and geometry. If you back-calculate Cd above 1, the entered flow, pressure, density, or diameters are inconsistent with this simplified liquid model.

Pressure-drop mode rearranges the same relationship to find the differential pressure required for a target flow. Throat-diameter mode solves the nonlinear equation numerically.

Worked Example 01

Water flow through a 100 mm x 50 mm Venturi

Known

Inlet diameter: 100 mm
Throat diameter: 50 mm
Differential pressure: 10 kPa
Density: 1000 kg/m³
Discharge coefficient: 0.98

Formula

Q = Cd A2 sqrt(2 Delta p / (rho (1 - beta^4)))

Substitution

Q = 0.98 x A2 x sqrt(2 x 10000 / [1000 x (1 - 0.5^4)])

Result

Q ≈ 0.00889 m³/s = 8.89 L/s = 31.99 m³/h

The throat velocity is about 4.53 m/s and the beta ratio is 0.50, a useful first-pass operating point for a liquid Venturi check.

Worked Example 02

Pressure drop for a target 8.89 L/s flow

Known

Flow rate: 8.89 L/s
Inlet diameter: 100 mm
Throat diameter: 50 mm
Density: 1000 kg/m³
Discharge coefficient: 0.98

Formula

Delta p = rho/2 (Q / (Cd A2))^2 (1 - beta^4)

Substitution

Delta p = 1000/2 x (0.00889 / (0.98 x A2))^2 x (1 - 0.5^4)

Result

Delta p ≈ 10.0 kPa

This is the same Venturi geometry solved in reverse. Pressure drop rises with the square of flow, so doubling flow would require about four times the differential pressure.

Applications

01Estimating liquid flow through a Venturi meter from differential pressure
02Finding pressure drop needed for a target flow through a known Venturi
03Sizing a preliminary throat diameter for a target liquid flow
04Back-calculating discharge coefficient from test data
05Comparing inlet and throat velocities for a proposed beta ratio

Assumptions

01Single-phase incompressible liquid flow.
02Pressure taps measure the differential pressure between the inlet section and throat.
03The Venturi is aligned with the pipe and represented by circular inlet and throat diameters.
04Discharge coefficient is known or estimated by the user and remains constant for the operating point.

Where This Model Stops

01Not for compressible gas, steam, flashing, cavitating, or two-phase flow.
02Not a certified ISO 5167 meter-sizing or custody-transfer calculation.
03Does not calculate Reynolds-number-dependent Cd correlations, permanent pressure loss, pressure recovery, cavitation margin, tap placement uncertainty, or upstream/downstream straight-run requirements.
04Very high velocities or large pressure drops require pump-system, erosion, noise, and cavitation checks outside this simplified tool.

References

[1]
Venturi Flow Rate Calculator
LMNO Engineering
Reference for incompressible Venturi flow equations and beta-ratio form.
[2]
Venturi Meter Calculator
Engineers Edge
Reference for Venturi differential-pressure flow calculation and velocity outputs.
[3]
Venturi Flow Calculator
Omni Calculator
Reference for user-facing Venturi pressure, diameter, density, and velocity context.

Frequently Asked Questions

How is this different from the Orifice Flow Calculator?

The Orifice Flow Calculator uses a simple opening equation, Q = Cd A sqrt(2 Delta p / rho). This Venturi Calculator includes the inlet-to-throat beta correction, 1 - beta^4, and reports inlet/throat velocities for a meter-style contraction.

What discharge coefficient should I use for a Venturi?

A clean, well-formed Venturi is often near Cd = 0.98, but the right value depends on geometry, taps, Reynolds number, installation, and calibration. Use manufacturer or test data when accuracy matters.

Can this calculator be used for air or steam?

No. This page is for incompressible liquids. Gas, air, and steam can require compressibility, expansion-factor, and choking checks.

What beta ratio is reasonable?

This calculator flags beta below 0.30 as low and above 0.75 as high. Those are screening hints only; certified meter design must follow the governing standard and manufacturer guidance.

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