Calculator Inputs
Use one method at a time. Results will appear above this form after submission.
Formula Used
1) Shear stress and density
u* = √(τ / ρ)
Here, τ is wall or surface shear stress and ρ is fluid density. This is the most direct friction velocity definition.
2) Reference velocity and drag coefficient
τ = 0.5 ρ Cd U²
u* = U √(Cd / 2)
Use this when drag coefficient and free-stream or reference velocity are known.
3) Neutral log profile
U(z) = (u* / κ) ln(z / z0)
u* = κ U(z) / ln(z / z0)
This method assumes a neutral boundary layer, steady conditions, and valid roughness representation.
Related turbulence quantity
-u'w' = τ / ρ = u*². The calculator reports this value in m²/s² for quick momentum-flux interpretation.
How to Use This Calculator
- Select the calculation method matching your available data.
- Enter density in the preferred unit system.
- Fill the fields required by the selected method.
- Choose decimals and graph sensitivity range.
- Click the calculate button.
- Read the result panel displayed above the form.
- Review the graph, derived stress, and shear classification.
- Use the CSV or PDF buttons to export results.
Example Data Table
| Case | Method | Inputs | Computed u* | Note |
|---|---|---|---|---|
| Wind tunnel wall test | Shear stress and density | τ = 0.45 Pa, ρ = 1.225 kg/m³ | 0.6061 m/s | Direct wall-shear estimate. |
| Open-air drag estimate | Velocity and drag coefficient | U = 12 m/s, Cd = 0.006 | 0.6573 m/s | Useful for bulk surface drag studies. |
| Neutral surface layer | Neutral log profile | U(z)=8.2 m/s, z=10 m, z0=0.03 m, κ=0.41 | 0.5942 m/s | Assumes neutral stratification. |
Frequently Asked Questions
1) What is friction velocity?
Friction velocity, written as u*, is a velocity scale derived from shear stress. It summarizes how strongly momentum is transferred near a wall or surface in turbulent flow.
2) Is friction velocity a real fluid speed?
Not exactly. It is a scaling velocity, not the actual fluid speed at one location. Engineers use it to describe near-wall turbulence and surface drag strength.
3) When should I use the shear-stress method?
Use it when wall shear stress and fluid density are known or measured. It is the most direct and least assumption-heavy method in this calculator.
4) When is the drag-coefficient method useful?
It works well when you know a representative velocity and bulk drag coefficient. That makes it practical for atmospheric surfaces, channels, and external-flow estimates.
5) What does the log-profile method assume?
It assumes a neutral boundary layer, appropriate roughness length, steady conditions, and a measurement point inside the logarithmic region of the flow profile.
6) Why must measurement height exceed roughness length?
Because the logarithm ln(z/z₀) must be defined and positive. If z is less than or equal to z₀, the log-law relation is physically invalid here.
7) What does the Reynolds stress output mean?
The reported value represents the equivalent momentum-flux term, often written as -u'w'. It equals u*² and helps interpret turbulence-driven shear transport.
8) Can I use this for air and water?
Yes. Enter the correct density and consistent inputs. The governing equations are general, though interpretation depends on the flow regime and surface condition.