skinfriction

Skinfriction, also called viscous drag, is the component of drag that arises from the viscous shear stress at the surface of a body moving through a fluid. It results from the velocity gradient in the fluid adjacent to the surface, within the boundary layer governed by the no-slip condition. The wall shear stress is tau_w = mu (du/dy) at the wall, where mu is the dynamic viscosity and du/dy is the velocity gradient perpendicular to the surface.

In engineering terms, skinfriction is often summarized by a dimensionless skin-friction coefficient Cf, defined as Cf = tau_w / (0.5 rho U^2), where rho is the fluid density and U is the free-stream velocity. For external flows over a flat plate, Cf depends on the local Reynolds number Re_x = U x / nu (nu being kinematic viscosity). Classic results include:

- Laminar flow: local Cf_x ≈ 0.664 / sqrt(Re_x) and plate-averaged Cf,L ≈ 1.328 / sqrt(Re_L).

- Turbulent flow: local Cf_x ≈ 0.0592 Re_x^(-1/5) and plate-averaged Cf,L ≈ 0.0592 Re_L^(-1/5) over a wide range of Re_L.

In internal flows, the term friction factor f (Darcy) serves a similar purpose for ducts and pipes, with laminar f = 64/Re and turbulent relations given by empirical correlations such as the Colebrook equation, which also incorporate surface roughness.

Skinfriction can be a substantial portion of total drag, especially for smooth, streamlined bodies at moderate to high Reynolds numbers, or for long surfaces like ship hulls and pipelines. It can be influenced by surface texture, flow regime, and boundary-layer transition. Techniques to reduce skinfriction include surface smoothing, riblets, laminar-flow control, and flow-control methods that delay transition or alter near-wall turbulence. Measurement methods include oil-film techniques, hot-wire anemometry near walls, and specialized wall-shear sensors.