Continuity Equation (Flow) Calculator
Work out continuity equation (flow) instantly with clear inputs, formula shown and shareable results.
About Continuity Equation (Flow) Calculator
For an incompressible fluid the volume passing every cross-section per second must be the same, so A1v1 = A2v2. Narrowing from 0.008 m2 to 0.002 m2 quadruples the speed from 2 to 8 m/s while the flow stays at 16 L/s. This is why a nozzle speeds up a hose and why river water races through a gorge.
Formulas
Continuity
A1 x v1 = A2 x v2
Flow rate
Q = A x v
Worked example
With the default values below, Continuity Equation (Flow) Calculator returns Velocity At Point 2 of 8.0000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Cross-sectional area at point 1minimum 0 m2
- 0.008 m2
- Velocity at point 1minimum 0 m/s
- 2 m/s
- Cross-sectional area at point 2minimum 0 m2
- 0.002 m2
Results
- Velocity At Point 2
- 8.0000 m/s
- Volumetric Flow Rate
- 0.01600 m3/s
- Same Flow In Litres Per Minute
- 960.00
- Speed Multiplication
- 4.000
Step by step
- 1Values used
- 2Continuity
- 3Flow rate
- 4Velocity At Point 2= 8.0000 m/s
- 5Volumetric Flow Rate= 0.01600 m3/s
- 6Same Flow In Litres Per Minute= 960.00
- 7Speed Multiplication= 4.000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Does this hold for gases?
Only at low speed. Above about Mach 0.3 density changes and the mass form rho.A.v must be used instead.
Why does pressure fall where speed rises?
Bernoulli's principle - the kinetic energy gained comes out of the pressure energy, which is what makes a venturi meter work.