CFD turbulence models need the first grid cell at the right distance from walls: y⁺ ≈ 1 to resolve the viscous sublayer, or 30–300 for wall functions. This calculator estimates that height before you build the mesh.
How to use the Y+ Calculator
- Free-stream velocity U
- Density ρ
- Dynamic viscosity μ
- Reference length L
- Desired y⁺
- Skin friction correlation
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the free-stream velocity, density, viscosity, reference length and target y⁺, and choose a skin-friction correlation.
Inputs explained
| Field | What to enter |
|---|---|
| Free-stream velocity U | Units: m/s, km/h, mph, ft/s, knots |
| Density ρ | Units: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³ |
| Dynamic viscosity μ | Units: Pa·s, mPa·s |
| Reference length L | Units: m, cm, mm, km, in, ft … |
| Desired y⁺ | A number |
| Skin friction correlation | Choose one: Schlichting, Prandtl (1/7 power), Granville, Schultz-Grunov |
What each result means
- Reynolds number = [Density ρ]×[Free-stream velocity U]×[Reference length L]÷[Dynamic viscosity μ]
- Wall shear stress = 0.5×[Skin friction coefficient]×[Density ρ]×[Free-stream velocity U]^2
- Friction velocity u* = sqrt([Wall shear stress]÷[Density ρ])
- First cell height = [Desired y⁺]×[Dynamic viscosity μ]÷([Density ρ]×[Friction velocity u×])
Example values
How the main result changes when Free-stream velocity U changes and everything else stays at the example values above:
| Free-stream velocity U (m/s) | First cell height (µm) |
|---|---|
| 10 | 32.9727 |
| 15 | 22.7923 |
| 20 | 17.5272 |
| 25 | 14.2912 |
| 30 | 12.0932 |
| 40 | 9.2881 |
Formula
Re = ρUL/μ, C_f from correlation, τ_w = ½C_f·ρU², u* = √(τ_w/ρ), y = y⁺·μ/(ρ·u*)
Worked example
Inputs — Free-stream velocity U: 20 m/s; Density ρ: 1.225 kg/m³; Dynamic viscosity μ: 1.81e-05 Pa·s; Reference length L: 1 m; Desired y⁺: 1; Skin friction correlation: Schlichting.
Results — Reynolds number = 1,353,591.16022; Skin friction coefficient = 0.00355; Wall shear stress = 0.87055 Pa; Friction velocity u* = 0.843 m/s; First cell height = 17.5272 µm.
Key terms
- y⁺
- Dimensionless wall distance, y·u*/ν.
Frequently asked questions
What y⁺ should I aim for?
About 1 for low-Re models like k-ω SST; 30–300 with wall functions.
Is the cell height the centroid or the face?
Many codes use the cell centroid – check your solver.
Why does the correlation matter?
Different flat-plate fits give slightly different C_f.
Should I check y⁺ after solving?
Yes – this is only an estimate.