Free · Physics models
Approximate CFD First-Cell Distance from y Plus
Estimate first-cell wall distance with disclosed empirical turbulent flat-plate skin-friction correlations.
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
reynolds number = 1.0000e+7; skin friction coefficient = 0.0029460. This worked example uses the displayed units and declared assumptions.
reynolds_number = density * freestream_velocity * length_boundary_layer / dynamic_viscosity; skin_friction_coefficient = reynolds_number >= 100000 ? (CfModel == 1 ? 0.074*reynolds_number^(-0.2) : CfModel == 2 ? (2*log10(reynolds_number)-0.65)^(-2.3) : CfModel == 3 ? 0.427*(log10(reynolds_number)-0.407)^(-2.64) : CfModel == 4 ? 0.0776*(log10(reynolds_number)-1.88)^(-2)+60/reynolds_number : 0.055*reynolds_number^(-0.182)) : 0; shear_stress = one_way(0.5 * skin_friction_coefficient * density * freestream_velocity * freestream_velocity); friction_velocity =one_way( (shear_stress/density)^0.5 ); wall_distance =one_way( yplus * dynamic_viscosity / (density * friction_velocity))
Worked example
Enter these known values and leave the other values blank.
- Freestream velocity (U==f==)
- 10 m/s
- Density (ρ)
- 1000 kg/m³
- Dynamic viscosity (μ)
- 1 mPa •s ·s
- Length of boundary layer (L)
- 1 m
- Dimensionless distance (y+)
- 1
- Skin friction coefficient approximation
- 1
- Reynold's number (Re)
- 10000000
- Skin friction coefficient (C==f==)
- 0.002946
- Shear stress (𝜏==w==)
- 147.3 Pa
- Friction velocity (u==*==)
- 0.3838 m/s
- Wall distance (y)
- 0.0026055 mm
Assumptions and limitations
- Flat-plate friction correlations give approximate average shear for smooth turbulent flow; the estimate omits pressure gradients, compressibility, roughness and transition. It is a starting mesh estimate, not a CFD convergence guarantee.
- The supported Reynolds range begins at100000 as a conservative calculation bound. Dynamic viscosity selectors carry a seconds suffix, so millipascal-seconds are correctly shown. Wall distance follows yν/uτ and must be checked against the solved wall stress.
Common questions
What assumptions apply?
Flat-plate friction correlations give approximate average shear for smooth turbulent flow; the estimate omits pressure gradients, compressibility, roughness and transition. It is a starting mesh estimate, not a CFD convergence guarantee.
Which unknowns can I solve?
Editable controls preserve the supported captured inverse branches. Clear the desired unknown and provide enough independent known quantities; singular or underdetermined inverses may remain incomplete.
References
Translate five captured empirical turbulent flat-plate friction correlations to local high-precision arithmetic. Retain selector coefficients and one output branch; require Reynolds number at least100000 as a conservative numerical/model lower bound. These are average flat-plate correlations used as approximate near-wall sizing, not local DNS wall stress. Finite turbulent correlation and physical material bounds.