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What is skin friction and how do I calculate the friction force of a fluid on a wall?
Skin friction arises from viscosity: the fluid sticks to the wall (zero velocity at the contact) and only recovers the free-stream velocity beyond the boundary layer. The shear stress τ = μ du/dy at the wall, integrated over the whole surface, gives the friction force F = ½ ρ V² S Cf. Its value depends on the regime of the boundary layer (laminar, then turbulent beyond Rex ≈ 5 × 10⁵), on the Reynolds number and on the roughness as soon as the asperities protrude from the viscous sublayer. In a pipe, this same friction produces the major head losses; in aerodynamics and naval hydrodynamics it forms the friction drag or viscous resistance, often the largest part on a streamlined body. Example: a surface of 1 m² swept by air at 20 m/s over 2 m of length undergoes 0.9 N of friction, with a boundary layer 38 mm thick at the trailing edge; in water, the same square metre at 2 m/s rubs with 8 N.
Skin friction formulas
- τ: wall shear stress, in Pa; μ: dynamic viscosity, in Pa·s; du/dy: velocity gradient at the wall, in s⁻¹
- F: friction force on the surface S (m²), in N; ρ: density, in kg/m³; V: free-stream velocity, in m/s
- Cf: mean friction coefficient, dimensionless; ReL = V L/ν based on the length L of the surface along the flow; in laminar flow Cf = 1.328/√ReL
- δ: thickness of the turbulent boundary layer at distance x from the leading edge, in m; Rex = V x/ν
- ν: kinematic viscosity μ/ρ, in m²/s (air at 20 °C: 15 × 10⁻⁶; water: 1.0 × 10⁻⁶)
Air friction on a 1 m² surface against speed
| Speed V | Reynolds ReL | Critical distance xc | Cf | Dynamic pressure ½ ρ V² | Friction force per m² |
|---|---|---|---|---|---|
| 10 m/s (36 km/h) | 1.3 × 10⁶ | 0.76 m | 0.0042 | 60 Pa | 0.26 N |
| 20 m/s (72 km/h) | 2.6 × 10⁶ | 0.38 m | 0.0038 | 241 Pa | 0.90 N |
| 30 m/s (108 km/h) | 4.0 × 10⁶ | 0.25 m | 0.0035 | 542 Pa | 1.9 N |
| 50 m/s (180 km/h) | 6.6 × 10⁶ | 0.15 m | 0.0032 | 1,505 Pa | 4.8 N |
Boundary layer thickness in air at 20 m/s
| Distance x from the leading edge | Rex | Regime | Thickness δ |
|---|---|---|---|
| 0.1 m | 1.3 × 10⁵ | laminar | 1.4 mm |
| 0.3 m | 4.0 × 10⁵ | laminar | 2.4 mm |
| 0.5 m | 6.6 × 10⁵ | turbulent | 13 mm |
| 1 m | 1.3 × 10⁶ | turbulent | 22 mm |
| 2 m | 2.6 × 10⁶ | turbulent | 38 mm |
Detailed explanations and calculation in Mecaflux
Friction on a flat surface or a pipe, slowing the fluid which is in contact with this surface. The greater is the distance between the surface and the fluid, the less friction effects are felt.. There is a certain distance where the effects of friction vanish and no longer disturb the movement of the fluid.The fluid zone, disturbed by surface friction, is the boundary layer, beyond the thickness of the boundary layer, it is considered that the fluid is not disturbed by the effect of friction surface.
The fluid in the boundary layer is disturbed and therefore slows down compared to fluid situated outside of the boundary layer..
boundary layer detail in mecaflux
In the ducts can be seen a maximum speed in the center of the fluid conduit and a speed decreasing to zero in intimate contact with the surface. To facilitate the calculation and manipulation of data an average speed is used.
Surface friction in the pipes are covered in the major head loss calculations
In naval hydrodynamics, the friction surface is called the viscous resistance, due to its dependence on the fluid viscosity parameter. in aerodynamics or hydrodynamics, The frictional resistance or viscous resistance constitutes only a part of the drag resistance.
The surface roughness is a determining factor for the strength of surface friction.With Mecaflux standard
In the interface drag and lift, choose flat plate for a detailed study of the boundary layer and surface friction.
Frequently asked questions
What is the difference between skin friction and form drag?
Skin friction is the tangential force due to viscosity in the boundary layer; it is proportional to the wetted surface and dominates on thin, streamlined bodies (wing at low angle of attack, slender hull, plate parallel to the flow). Form (or pressure) drag comes from the separated wake behind a bluff body; it is proportional to the frontal area and dominates on a sphere, a cylinder or a plate normal to the flow. The total drag is the sum of both.
How does roughness act on friction?
As long as the asperities stay within the viscous sublayer, the wall is "hydraulically smooth" and the friction depends only on the Reynolds number: this is the case if their height stays below about 100 ν/V, i.e. 75 µm in air at 20 m/s and 50 µm in water at 2 m/s. Beyond that, the friction coefficient rises and becomes independent of the Reynolds number, exactly like the friction factor λ of a rough pipe in the Colebrook equation.
How can skin friction be reduced?
By reducing the wetted surface, polishing the surface until it is hydraulically smooth, delaying transition to turbulence (laminar sections, carefully made leading edge) and, for a ship, keeping the hull clean: fouling can increase friction by half. Since friction grows with the square of the speed, reducing the speed by 10 % saves nearly 20 % of the force and 27 % of the power.
How do I calculate the skin friction of my own project?
In the drag and lift tab of Mecaflux Standard, the flat plate study gives the friction force, the boundary layer thickness and the transition distance for the length, width, speed and fluid of your choice; for a pipe, the friction appears in the major head loss calculation. Heliciel computes the friction of each blade, wing or hull section from the polar of its aerofoil at the local Reynolds number. For a vehicle, a ship or a machine to optimise, Mecaflux carries out the study of your project, or offers training on the software applied to your own project.