Which law is followed by the velocity distribution in the turbulent boundary layer?

ANS:C - Logarithmic law

The velocity distribution in the turbulent boundary layer typically follows the logarithmic law.

Explanation:

1. Turbulent Boundary Layer:
   • In a turbulent boundary layer, which forms on a surface when a fluid flows over it, the velocity profile across the boundary layer is characterized by fluctuations and eddies (turbulence).
2. Logarithmic Law:
   • According to the logarithmic law (also known as the logarithmic velocity profile), the velocity U(y)U(y)U(y) at a distance yyy from the wall in the turbulent boundary layer can be expressed as: U(y)=uτκln⁡(yy0)+BU(y) = \frac{u_\tau}{\kappa} \ln\left(\frac{y}{y_0}\right) + BU(y)=κuτ​​ln(y0​y​)+B where:
     • uτu_\tauuτ​ is the shear velocity,
     • κ\kappaκ is the von Kármán constant (approximately 0.41),
     • yyy is the distance from the wall,
     • y0y_0y0​ is the roughness length or displacement thickness,
     • BBB is a constant.
3. Other Laws:
   • Parabolic Law: This describes the velocity profile in laminar flow, where the velocity distribution is parabolic across the boundary layer. It is not applicable to turbulent flow.
   • Linear Law: This describes the velocity profile in very thin viscous sub-layers near the wall in turbulent flow, where velocity varies linearly with distance from the wall. It does not describe the overall velocity distribution across the turbulent boundary layer.
   • None of These: While the parabolic and linear laws apply to specific flow conditions, they do not describe the velocity distribution in a turbulent boundary layer.

Conclusion: