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First Cell Height Calculator

Compute wall-to-cell-centre distance and full first-layer height using y+, viscosity, friction velocity, and cell-centre fraction.

First Cell Height inputs

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.

Fluid properties

Fluid property mode

Fluid preset

Viscosity mode

Density

Density unit

Kinematic viscosity

Kinematic viscosity unit

Water near 20 °C, 20 °C, approximately 1 atm. Water properties vary with temperature, pressure, dissolved material, and source. Override the preset for real design or validation work.

Wall treatment inputs

Target Y plus

Cell-centre fraction

Use 0.5 when the centre is halfway through the first layer.

Output length unit

Friction velocity mode

Friction velocity

Friction velocity unit

Display precision

Result section

warningdirect

Full first-cell height

0.04 mm

Secondary results

Wall-to-cell-centre distance: 0.02 mm
Centre distance in meters: 2.00000e-5 m
Full first-cell height in meters: 4.00000e-5 m
Friction velocity: 0.05 m/s
Target Y plus: 1

Unit conversion summary

Unit-normalization summary: 1.00000e-6 m^2/s; 0.05 m/s

Warnings

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.
Fluid presets are starter values only; verify properties at the actual operating condition.
One first-cell height may not satisfy the target everywhere because local wall shear varies over the surface.

Assumptions

Cell-centre fraction is measured from the wall and defaults to 0.5 for a simple centred first cell.
Actual achieved y plus must be checked after solving.

Calculation steps

Calculate cell-centre wall distance2.00000e-5 m
Convert centre distance to full first-layer height4.00000e-5 m

First cell height from target Y plus

y = y^+\nu/u_\tau;\quad \Delta y_1 = y/c

y = y+ nu / u_tau; Delta y1 = y / c

y = 1 x 1.00000e-6 m^2/s / 0.05 m/s

Delta y1 = 2.00000e-5 m / 0.5

Method comparison table

CFD result comparison table
Quantity	Value
Full height in meters	4.00000e-5 m
Full height in millimeters	0.04 mm
Full height in micrometers	40 µm
Full height in inches	0.0015748 in

Technical visual

Technical sketch for first cell height calculator. Values are illustrative; calculated values appear in the result section.

Engineering interpretation

Use this as a preliminary near-wall mesh estimate, then verify achieved y plus after a CFD solution.

What is the first cell height calculator?

Estimate the first near-wall cell height required for a target y plus and distinguish centre distance from full first-layer height.

How to use the first cell height calculator

Select the calculation mode that matches the data you already have.
Enter values with units; the calculator normalizes inputs to SI internally.
Review derived values, warnings, formulas, and assumptions before using the result in another CFD step.
After solving, check achieved y plus and revise the mesh if local wall shear differs.

Input explanations

Target y plus defines the desired dimensionless wall distance.
Cell-centre fraction defaults to 0.5 for a simple centred first cell.
Full first-layer height is Delta y1 = y/c.

Notation

Formula notation
Symbol	Meaning	Unit
y+	Target dimensionless wall distance	dimensionless
y	Wall-to-cell-centre distance	m
Delta y1	Full first-layer height	m
c	Cell-centre fraction	dimensionless
u_tau	Friction velocity	m/s

Worked examples

Target y+ = 1, u_tau = 0.05 m/s, nu = 1e-6 m^2/s, c = 0.5 gives full height 4e-5 m.

Target y+ = 30, u_tau = 0.5 m/s, nu = 1.5e-5 m^2/s, c = 0.5 gives full height 0.0018 m.

Custom c: full first-layer height is always centre distance divided by c.

Cross-tool workflow

The First Cell Height Calculator supports direct, wall-shear, Darcy-factor, and skin-friction modes for preliminary inflation-layer planning.

Check achieved Y Plus

Common mistakes

Assuming y plus 1 is always required.
Forgetting to double centre distance when c = 0.5.
Using one first-cell height for a surface with large wall-shear variation.
Not checking achieved y plus after solving.

Limitations

This is a preliminary mesh estimate.
Boundary-layer growth rate and number of inflation layers are not solved.
Curvature, separation, transition, compressibility, roughness, and heat transfer can alter requirements.

References

White Fluid Mechanics: White, F. M., Fluid Mechanics, McGraw-Hill.
Fox and McDonald Fluid Mechanics: Fox, McDonald, and Pritchard, Introduction to Fluid Mechanics, Wiley.
Versteeg and Malalasekera CFD: Versteeg, H. K. and Malalasekera, W., An Introduction to Computational Fluid Dynamics, Pearson.
Pope Turbulent Flows: Pope, S. B., Turbulent Flows, Cambridge University Press.
NASA Turbulence Modeling Resource: NASA Langley Research Center, Turbulence Modeling Resource.

How is first-cell height calculated?

First calculate centre distance y = y+ nu / u_tau, then full height Delta y1 = y/c.

Why is the result twice the cell-centre distance?

When c = 0.5, the cell centre is halfway through the first layer, so full height is 2y.

Is y plus 1 always required?

No. Target y plus depends on turbulence model and wall treatment.

Must achieved y plus be checked after solving?

Yes. This is only a pre-solve estimate.

Does one first-cell height work over the entire wall?

Not always, because local wall shear varies spatially.

Can I use wall shear stress?

Yes. Wall-shear mode derives friction velocity from tau_w and density.

Does this set inflation growth rate?

No. Growth rate and layer count are outside this phase.

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Engineering disclaimer

This tool is intended for educational, estimation, and preliminary CFD setup support. Always verify critical engineering calculations with applicable standards, validated software, solver documentation, and qualified professional judgment.

Need Professional Support?

ScholarTool is powered by ScholarEase Consultancy Services LLP. Professional engineering, simulation, research, and technical documentation support is available through the connected services website.

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Last reviewed: 2026-06-19

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First Cell Height inputs

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.

Fluid properties

Fluid property mode

Fluid preset

Viscosity mode

Density

Density unit

Kinematic viscosity

Kinematic viscosity unit

Water near 20 °C, 20 °C, approximately 1 atm. Water properties vary with temperature, pressure, dissolved material, and source. Override the preset for real design or validation work.

Wall treatment inputs

Target Y plus

Cell-centre fraction

Use 0.5 when the centre is halfway through the first layer.

Output length unit

Friction velocity mode

Friction velocity

Friction velocity unit

Display precision

Result section

warningdirect

Full first-cell height

0.04 mm

Secondary results

Wall-to-cell-centre distance: 0.02 mm
Centre distance in meters: 2.00000e-5 m
Full first-cell height in meters: 4.00000e-5 m
Friction velocity: 0.05 m/s
Target Y plus: 1

Unit conversion summary

Unit-normalization summary: 1.00000e-6 m^2/s; 0.05 m/s

Warnings

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.
Fluid presets are starter values only; verify properties at the actual operating condition.
One first-cell height may not satisfy the target everywhere because local wall shear varies over the surface.

Assumptions

Cell-centre fraction is measured from the wall and defaults to 0.5 for a simple centred first cell.
Actual achieved y plus must be checked after solving.

Calculation steps

Calculate cell-centre wall distance2.00000e-5 m
Convert centre distance to full first-layer height4.00000e-5 m

First cell height from target Y plus

y = y^+\nu/u_\tau;\quad \Delta y_1 = y/c

y = y+ nu / u_tau; Delta y1 = y / c

y = 1 x 1.00000e-6 m^2/s / 0.05 m/s

Delta y1 = 2.00000e-5 m / 0.5

Method comparison table

CFD result comparison table
Quantity	Value
Full height in meters	4.00000e-5 m
Full height in millimeters	0.04 mm
Full height in micrometers	40 µm
Full height in inches	0.0015748 in

How to use the first cell height calculator

Select the calculation mode that matches the data you already have.
Enter values with units; the calculator normalizes inputs to SI internally.
Review derived values, warnings, formulas, and assumptions before using the result in another CFD step.
After solving, check achieved y plus and revise the mesh if local wall shear differs.

Symbol

Meaning

Unit

Target dimensionless wall distance

dimensionless

Wall-to-cell-centre distance

Delta y1

Full first-layer height

Cell-centre fraction

dimensionless

u_tau

Friction velocity

m/s

References

White Fluid Mechanics: White, F. M., Fluid Mechanics, McGraw-Hill.

Fox and McDonald Fluid Mechanics: Fox, McDonald, and Pritchard, Introduction to Fluid Mechanics, Wiley.

Versteeg and Malalasekera CFD: Versteeg, H. K. and Malalasekera, W., An Introduction to Computational Fluid Dynamics, Pearson.

Pope Turbulent Flows: Pope, S. B., Turbulent Flows, Cambridge University Press.

NASA Turbulence Modeling Resource: NASA Langley Research Center, Turbulence Modeling Resource.

First Cell Height inputs

Fluid properties

Wall treatment inputs

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

First cell height from target Y plus

Method comparison table

Technical visual

Engineering interpretation

What is the first cell height calculator?

How to use the first cell height calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Professional support from ScholarEase Consultancy Services LLP

Print summary

Engineering disclaimer

Need Professional Support?

First Cell Height inputs

Fluid properties

Wall treatment inputs

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

First cell height from target Y plus

Method comparison table

Technical visual

Engineering interpretation

What is the first cell height calculator?

How to use the first cell height calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Professional support from ScholarEase Consultancy Services LLP

Print summary

Engineering disclaimer

Need Professional Support?