The ratio of the coefficient of friction drag in laminar boundary layer compared to that in turbulent boundary layer is proportional to:

The coefficient of friction drag is a measure of the resistance or drag experienced by a fluid moving over a solid surface. In the context of boundary layers, it refers to the frictional forces acting between the fluid and the boundary layer. The ratio of the coefficient of friction drag in laminar boundary layer compared to that in turbulent boundary layer depends on several factors.

Reynolds Number:
The Reynolds number (Re) is a dimensionless quantity that characterizes the flow regime. It is defined as the ratio of inertial forces to viscous forces. The Reynolds number is given by the equation Re = ρUL/μ, where ρ is the density of the fluid, U is the velocity of the fluid, L is a characteristic length, and μ is the dynamic viscosity of the fluid. The Reynolds number determines whether the flow is laminar or turbulent. For low Reynolds numbers (Re < 2000),="" the="" flow="" is="" typically="" laminar,="" while="" for="" high="" reynolds="" numbers="" (re="" /> 4000), the flow is turbulent.

Transition from Laminar to Turbulent Flow:
When the Reynolds number exceeds a critical value (typically around 2000-4000), the flow transitions from laminar to turbulent. In laminar flow, the fluid particles move in smooth, parallel layers, while in turbulent flow, the fluid particles move in a chaotic and irregular manner. The transition from laminar to turbulent flow is influenced by factors such as surface roughness, pressure gradients, and disturbances in the flow.

Effect on Coefficient of Friction Drag:
The coefficient of friction drag is higher in a laminar boundary layer compared to a turbulent boundary layer. This is because laminar flow has a more orderly and streamlined flow profile, leading to a larger area of contact between the fluid and the solid surface. In contrast, turbulent flow has eddies and swirls, which create a more disrupted flow profile and reduce the area of contact between the fluid and the solid surface.

As a result, the frictional forces acting between the fluid and the boundary layer are higher in laminar flow, leading to a higher coefficient of friction drag. In turbulent flow, the eddies and swirls mix the fluid and reduce the frictional forces, resulting in a lower coefficient of friction drag.

Proportional Relationship:
The ratio of the coefficient of friction drag in laminar boundary layer compared to that in turbulent boundary layer is proportional to the Reynolds number. As the Reynolds number increases, the flow transitions from laminar to turbulent, and the ratio of the coefficient of friction drag decreases. This relationship can be expressed as:

Ratio of coefficient of friction drag (laminar) / Ratio of coefficient of friction drag (turbulent) ∝ Reynolds number

In conclusion, the ratio of the coefficient of friction drag in laminar boundary layer compared to that in turbulent boundary layer depends on the Reynolds number. Higher Reynolds numbers result in a lower ratio, indicating a higher coefficient of friction drag in laminar flow compared to turbulent flow.