Boundary Layer Calculator
Air at 10 m/s over a flat plate grows a laminar boundary layer 4.272 mm thick at 0.5 m from the leading edge.
Air at 15 °C 1.46 × 10⁻⁵, water at 20 °C 1.0 × 10⁻⁶ m²/s.
4.27200187265877 mm
Full answer, then cut to fewer decimals (not rounded):
- 4.27200187265877 mm
- 4.2720018726587 mm
- 4.272001872658 mm
- 4.27200187265 mm
- 4.2720018726 mm
- 4.272001872 mm
- 4.27200187 mm
- 4.2720018 mm
- 4.272001 mm
- 4.27200 mm
- 4.2720 mm
- 4.272 mm
- 4.27 mm
- 4.2 mm
- Reynolds number Reₓ = Ux/ν
- 342465.7534
- Regime used
- laminar (Blasius)
- Displacement thickness δ*
- 1.470252164 mm
- Momentum thickness θ
- 0.5673218487 mm
- Shape factor H = δ*/θ
- 2.591566265
- Local skin-friction coefficient c_f
- 0.001134643697
- Average skin-friction coefficient (plate length x)
- 0.002269287395
Step-by-step solution
- Reₓ = Ux ÷ ν = 10 × 0.5 ÷ 0.0000146 = 342465.7534
- δ = 5x ÷ √Reₓ = 4.272001873 mm
- c_f = 0.664 ÷ √Reₓ = 0.001134643697
Boundary Layer Formula
Laminar: δ = 5x/√Reₓ, c_f = 0.664/√Reₓ
δ* = 1.7208x/√Reₓ, θ = 0.664x/√Reₓ; turbulent δ = 0.37x/Reₓ^0.2, c_f = 0.0592/Reₓ^0.2
Worked Example
Air at 10 m/s, 0.5 m from the leading edge (ν = 1.46 × 10⁻⁵ m²/s):
- Reₓ = Ux ÷ ν = 10 × 0.5 ÷ 0.0000146 = 342465.7534
- δ = 5x ÷ √Reₓ = 4.272001873 mm
- c_f = 0.664 ÷ √Reₓ = 0.001134643697
Regime used: laminar (Blasius) · Displacement thickness δ*: 1.470252164 mm · Momentum thickness θ: 0.5673218487 mm · Shape factor H = δ*/θ: 2.591566265 · Local skin-friction coefficient c_f: 0.001134643697 · Average skin-friction coefficient (plate length x): 0.002269287395
GATE tip
Laminar δ grows as √x and turbulent δ as x^0.8. The shape factor H = δ*/θ is 2.59 for Blasius and about 1.3 for a turbulent layer, a common identification question.
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Frequently asked questions
When does the boundary layer become turbulent?
On a smooth flat plate around Reₓ = 5 × 10⁵, though disturbances, roughness and pressure gradients can move it anywhere from 10⁵ to 3 × 10⁶.
What is displacement thickness?
How far the outer flow is pushed away by the slower fluid near the wall: about a third of δ in a laminar layer.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Boundary Layer Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/boundary-layer-calculator/
IEEE
Scientific Converters, "Boundary Layer Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/boundary-layer-calculator/