Calculator · Fluid Mechanics
Continuity Equation Calculator
For one steady incompressible stream the same volumetric flow rate passes every cross-section, so a narrower section must run faster. State three of the four quantities and the fourth follows.
Inputs
Both sections lie on one flow path with the same flow direction, so speeds and flow rates here are magnitudes. Zero flow is a valid state.
Results
Downstream speed V₂ = A₁V₁/A₂
Solved from steady incompressible continuity along a single stream.
| Upstream area A₁ | 0.01 m² |
|---|---|
| Upstream speed V₁ | 2 m/s |
| Downstream area A₂ | 0.005 m² |
| Downstream speed V₂ | 4 m/s |
| Volumetric flow rate Q | 0.02 m³/s |
| Area ratio A₁/A₂ | 2 |
Assumptions
- · Steady, incompressible, single-stream flow: the same Q passes both sections.
- · Both sections are on one flow path with the same flow direction.
Explore in the Lab
The same areas and flow rate become the stations of one energy path.
Technical reference
Q = A V
A₁ V₁ = A₂ V₂
- A
- flow area of the cross-section[m²]
- V
- mean speed over that area[m/s]
- Q
- volumetric flow rate common to both sections[m³/s]
Continuity in this form holds for steady incompressible flow of one stream. Branches, storage and compressible gas flow are outside it.
V is the mean speed over the section, not a local or centreline speed. A velocity profile changes the kinetic energy, not the flow rate.
Stating all four quantities at once overconstrains the problem. If A₁V₁ and A₂V₂ disagree, the calculator says so rather than choosing a winner.