Reynolds Number and Boundary Layer Transition

Reynolds number (Re) is a dimensionless quantity that describes the relative importance of inertial and viscous forces in a flow. It is defined as the ratio of inertial forces to viscous forces and is given by the equation:

Re = ρVD/μ

where ρ is the density of the fluid, V is the velocity of the fluid, D is the characteristic length of the flow (e.g., diameter of a pipe), and μ is the dynamic viscosity of the fluid.

Boundary Layer Transition

The boundary layer is a thin layer of fluid adjacent to a solid surface where the velocity of the fluid goes from zero at the surface to the free stream velocity. In external flows, the boundary layer can either be laminar or turbulent depending on the value of Reynolds number. The transition from laminar to turbulent boundary layer is an important phenomenon in fluid mechanics and is characterized by the formation of eddies and turbulence in the flow.

Critical Reynolds Number

The critical Reynolds number for transition from laminar to turbulent boundary layer in external flows is typically taken as 5x10^5. This value is based on experimental observations and is valid for a wide range of flow conditions.

However, it should be noted that the critical Reynolds number is not a sharp transition point and can vary depending on the surface roughness, pressure gradient, and other factors. In some cases, the transition can occur at lower Reynolds numbers, while in other cases it can occur at higher Reynolds numbers.

Applications

The knowledge of critical Reynolds number is important in the design of engineering systems that involve fluid flows, such as aircraft wings, wind turbines, and pipelines. By knowing the critical Reynolds number, engineers can predict the onset of turbulence and design systems that can operate in either laminar or turbulent regimes, depending on the desired performance characteristics.

A laminar boundary layer over a flat plate eventually becomes turbulent over certain range of Reynolds number. There is no unique value pf Reynolds number, for this change to happen. It mainly depends on the free stream turbulence and surface roughness parameters. With a very fine polished wall and with a quiet free stream, one can delay the transition. A controlling parameter such as the critical Reynolds number of transition may be defined. On a flat plate with a sharp leading edge in a typical free stream air flow, the transition occurs between the Reynolds number ranges of (2 x10^5 to 3 x 10^6 )
So the transitional Reynolds number is normally taken as 5 X 10^5. option c is correct