Formula & Calculator
Laminar Flat Plate Skin Friction Coefficient
Local skin-friction coefficient for laminar boundary-layer flow over a flat plate (Blasius solution).
Interpretation
Laminar flat plate skin friction coefficient: C_f = 1.328 / √(Re_x), where Re_x is the local Reynolds number. It gives the local skin friction for laminar flow. Example: Re_x=1e6 → C_f = 1.328/1000 = 0.001328.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| C_f | Skin friction coefficient | |
| Re_x | Local Reynolds number |
What it means
This relation, from the Blasius solution, gives the local skin friction coefficient for laminar boundary layer flow over a flat plate. It is valid for Reynolds numbers up to the transition point. The coefficient decreases with the square root of Re_x. This formula is used to calculate the shear stress and thus the viscous drag on surfaces. In aerodynamic design, it helps estimate skin friction drag. Understanding this relation is essential for boundary layer analysis and for predicting drag contributions. It also serves as a benchmark for validating CFD codes.
Worked example
Laminar Skin Friction – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Re_x | 1×10⁵ |
| Parameter | Value |
|---|---|
| Re_x | 5×10⁵ |
Common mistakes
- Laminar flat plate skin friction coefficient: C_f = 1.328 / √Re_x.
- Re_x: Local Reynolds number based on distance x from leading edge.
- Valid for laminar flow over a flat plate at zero pressure gradient.
- Transition to turbulent occurs around Re_x ≈ 5×10⁵.
- Units: dimensionless.
Applications
The laminar flat plate skin friction coefficient, C_f = 1.328/√(Re_x), is derived from Blasius solution for laminar boundary layer on a flat plate. It is used to estimate the friction drag contribution for laminar flow. Engineers apply this in preliminary aerodynamic design, especially for aircraft with smooth surfaces and low Reynolds numbers (e.g., gliders, UAVs). It also forms the basis for transition prediction. By understanding laminar friction, aerospace engineers can assess the potential drag reduction from maintaining laminar flow through careful surface design, leading to improved efficiency and range.
- Drag estimation for gliders and laminar‑flow aircraft
- Boundary layer transition and laminar flow control
- Wind tunnel model friction drag evaluation
- Surface roughness and contamination effects on drag
- Early‑stage aerodynamic sizing and performance assessment
Frequently Asked Questions
It gives the local skin‑friction coefficient for laminar boundary‑layer flow over a flat plate, from the Blasius solution. It is used to compute shear stress and drag.
Cf = local skin‑friction coefficient (dimensionless)
Rex = Reynolds number based on distance x from the leading edge
It is essential for predicting drag on streamlined bodies, such as aircraft wings and fuselages, when the boundary layer is laminar.
It applies only for laminar flow on a smooth flat plate with zero pressure gradient. It is not valid for turbulent flow or for surfaces with roughness.
- Applying this laminar relation beyond the transition Reynolds number (~5×105), where flow becomes turbulent.
- Using the average skin friction coefficient instead of the local value.
- Ignoring the effect of pressure gradient.
At x = 1 m from leading edge, with freestream velocity V = 10 m/s, kinematic viscosity ν = 1.5×10⁻⁵ m²/s. Rex = V·x/ν = 10×1/1.5e−5 = 6.67×10⁵. Cf = 1.328 / √(6.67×10⁵) = 1.328 / 816.5 ≈ 0.00163.
Integrate the local shear stress τw = ½ρV²·Cf over the plate surface. The average Cf for laminar flow is twice the local value at the end.
Cf decreases as Rex increases, following a 1/√Re relation. This means that for longer plates, the friction coefficient decreases.
It is the exact similarity solution of the laminar boundary layer equations for a flat plate, giving velocity profiles and wall shear.
After transition to turbulent flow, Cf becomes higher (roughly 0.074/Rex^(1/5)) and the drag increases significantly.