Flow Measurement · Glossary

What is Bernoulli's Equation?

energy balance along a streamlineFlow Measurement

Bernoulli's equation states that pressure, kinetic and elevation energy along a streamline add up to a constant in ideal flow.

Bernoulli's Equation Explained

When fluid speeds up through a restriction its pressure falls, and when it slows down the pressure rises again. This trade between pressure and velocity is the basis of orifice, venturi, nozzle and pitot measurement.

Real fluids lose some energy to friction, so practical equations add a discharge coefficient and, for gases, an expansibility factor.

Bernoulli's Equation Formula

p + ½ ρ v² + ρ g h = constant

p	static pressure (Pa)
ρ	density (kg/m³)
v	velocity (m/s)
g	9.80665 m/s²
h	elevation (m)

Example: Water speeding up from 1 to 3 m/s at the same height loses ½ × 1000 × (3² − 1²) = 4000 Pa, or 40 mbar, of static pressure.

Calculators for Bernoulli's Equation

CalculatorOrifice Flow CalculatorFree online calculator with formula and worked example.CalculatorVenturi Flow CalculatorFree online calculator with formula and worked example.CalculatorPitot Tube CalculatorFree online calculator with formula and worked example.

Frequently Asked Questions

What is Bernoulli's Equation?

Bernoulli's equation states that pressure, kinetic and elevation energy along a streamline add up to a constant in ideal flow.

Why does flow vary with the square root of DP?

From Bernoulli, DP across a restriction is proportional to velocity squared, so velocity and flow are proportional to √DP.

Does Bernoulli work for gases?

For small pressure changes, yes. For larger changes gas density changes, which ISO 5167 handles with the expansibility factor.

Learn more on the blog

Mistakes in DP flow measurement

A practical guide on instrumentationblog.in with more detail on Bernoulli's equation and how it is applied on real plants.

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More Flow Measurement Terms

Flow termBeta RatioBeta ratio is the bore diameter of an orifice, nozzle or venturi throat divided by the pipe internal diameter.Flow termExpansibility FactorExpansibility factor corrects DP flow equations for the drop in gas density as gas expands through the…Flow termPermanent Pressure LossPermanent pressure loss is the part of the DP across a flow element that is not recovered downstream and…Flow termSquare Root ExtractionSquare root extraction converts a DP signal into a linear flow signal, because flow through a DP element…Flow termTurndown RatioTurndown ratio is the maximum flow divided by the minimum flow a meter can measure within its stated accuracy.Flow termLow Flow CutoffLow flow cutoff forces the flow reading to zero below a set value, so noise and zero drift do not show as…

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