What is the effect of surface roughness on the friction drag coefficient in laminar and turbulent flows?

In fluid dynamics, friction drag is caused by the resistance of the fluid that comes in contact with the surface of an object moving through the fluid. The friction drag coefficient is a dimensionless number that characterizes the intensity of drag force encountered by the object. Surface roughness affects the friction drag coefficient in both laminar and turbulent flows. Let's have a look at each case separately.

In laminar flows, the fluid particles move smoothly along parallel streamlines, and the velocity of the fluid at the surface of the object is zero (no-slip condition). The viscous action of the fluid dominates in this regime, and the influence of surface roughness on the friction drag coefficient is considered negligible. Even though roughness might cause local flow separation and destabilization, for sufficiently smooth surfaces, the overall effect on the friction drag coefficient is minimal.

In turbulent flows, the fluid moves in an irregular and chaotic manner with rapid fluctuations, eddies, and vortices, leading to an increase in the overall drag force. Surface roughness becomes more significant in turbulent flows, as it contributes to the generation of turbulent eddies, increases the fluid shear stress, and causes momentum transfer between fluid layers.

The effect of surface roughness on the friction drag coefficient in turbulent flows can be expressed in four different regimes, depending on the ratio of roughness height to boundary layer thickness: 1. Hydrodynamically smooth: For very low surface roughness compared to the boundary layer thickness, turbulent eddies are not affected by the roughness, and the friction drag coefficient remains virtually unchanged. 2. Transitionally rough: As surface roughness increases, turbulence starts to be affected by the roughness elements, and the friction drag coefficient begins to increase. 3. Fully rough: In this regime, the turbulence is significantly influenced by the roughness elements, leading to a substantial increase in the friction drag coefficient. In this case, the friction drag coefficient is independent of the fluid's viscosity and depends only on the roughness height. 4. Very rough: In this case, the roughness elements protrude into the outer layer of turbulence, and the effect of roughness becomes even more pronounced. The no-slip condition is often violated, leading to separation and even higher friction drag coefficients.

Surface roughness has a significant effect on the friction drag coefficient in turbulent flows but negligible effect in the laminar flow regime. In turbulent flows, the friction drag coefficient increases with increasing surface roughness, especially in fully rough and very rough regimes. In contrast, in laminar flows, surface roughness plays a minor role due to the dominance of viscous forces.