Enter the velocity and the stream function into the calculator to determine the potential flow. This calculator can also evaluate any of the variables given the others are known.
- All Physics Calculators
- Pipe Flow Calculator
- Water Flow Rate Calculator
- Volumetric Flow Rate Calculator
- Flow Rate Pressure Calculator
- Stream Velocity Calculator
- Venturi Effect Calculator
Potential Flow Formula
This calculator uses a simplified relationship between velocity and a stream-function input to compute a derived potential value. It is most useful when your course material, worksheet, or engineering method explicitly defines the quantity with the relation below.
\phi = V \cdot \psi
| Variable | Meaning | Typical Units |
|---|---|---|
| φ | Calculated potential value returned by the calculator | Depends on your problem definition |
| V | Velocity or signed flow speed | m/s, ft/s, km/h, mph |
| ψ | Stream function or application-specific flow-function input | m²/s or ft²/s when defined that way |
Equivalent Forms
If you know the potential value and one of the other variables, the same relationship can be rearranged to solve for the missing quantity.
V = \frac{\phi}{\psi}\psi = \frac{\phi}{V}How to Use the Calculator
- Choose one consistent unit system before entering values.
- Enter any two known quantities.
- Calculate the unknown value.
- Keep the sign convention consistent if direction matters in your problem.
- When solving for velocity or stream function, make sure the denominator is not zero.
Example
If the velocity is 5 and the stream-function input is 2, the calculated result is:
\phi = 5 \cdot 2 = 10
Interpret the result using the same unit framework and variable definition used in your source problem.
How the Result Changes
- If velocity increases while the stream-function input stays fixed, the calculated potential increases proportionally.
- If the stream-function input increases while velocity stays fixed, the result also increases proportionally.
- Doubling either input doubles the output.
- If one input is negative, the result becomes negative.
- If velocity is zero, the computed potential is zero for this algebraic model.
Important Theory Note
In classical fluid mechanics, potential flow refers to ideal, incompressible, irrotational flow. In that setting, the velocity potential and stream function are connected through spatial derivatives, not a simple product.
u = \frac{\partial \phi}{\partial x} = \frac{\partial \psi}{\partial y}v = \frac{\partial \phi}{\partial y} = -\frac{\partial \psi}{\partial x}\nabla^2 \phi = 0
That means this calculator should be used when your problem specifically defines the desired output with the simplified relation at the top. If your ψ value is the classical stream function, the computed product should be treated as a custom derived quantity unless your text or method defines it otherwise.
When This Calculator Is Useful
- Quick educational checks using a predefined algebraic relationship.
- Comparing cases where velocity changes and the stream-function input is already known.
- Internal worksheets or simplified models that use a single scalar output instead of a full flow-field solution.
Common Mistakes to Avoid
- Mixing SI and Imperial units without converting first.
- Assuming the formula represents the full physics of potential-flow theory in every situation.
- Ignoring the sign of the inputs when direction matters.
- Trying to solve for velocity or stream function when the divisor is zero.
- Interpreting one calculator output as a complete pressure, streamline, or velocity-field analysis.
Quick FAQ
Can the answer be negative?
Yes. The sign of the result follows the sign convention of the input values.
Do the units need to match?
Yes. Use a consistent system throughout the calculation so the output remains meaningful.
Is this the same as solving a true potential-flow field?
No. A full potential-flow analysis requires governing equations and boundary conditions across the flow domain, while this calculator evaluates a single simplified relationship.
