Prandtl mixing length is

ANS:C - zero at the pipe wall.

Prandtl's mixing length is applicable to turbulent flow problems. Here's an explanation:

1. Definition: Prandtl's mixing length concept is used in fluid mechanics to model turbulent flow, specifically in the context of the eddy viscosity hypothesis.
2. Turbulent Flow: Turbulent flow is characterized by irregular fluctuations in velocity and pressure within the fluid. These fluctuations create small-scale vortices or eddies that enhance mixing and transport properties within the flow.
3. Mixing Length Theory: Prandtl introduced the concept of mixing length (lll) as a measure of the size of eddies in turbulent flow. It is defined as the characteristic length scale over which momentum is transferred between fluid layers due to turbulent eddies. The mixing length theory assumes that the eddy viscosity μt\mu_tμt​ can be related to the mixing length: μt=ρ⋅l⋅dudy\mu_t = \rho \cdot l \cdot \sqrt{\frac{du}{dy}}μt​=ρ⋅l⋅dydu​​ where:
   • μt\mu_tμt​ is the turbulent eddy viscosity,
   • ρ\rhoρ is the density of the fluid,
   • lll is the mixing length,
   • dudy\frac{du}{dy}dydu​ is the velocity gradient perpendicular to the flow direction.
4. Applicability: Prandtl's mixing length theory is specifically developed for turbulent flow problems where the assumption of eddy viscosity plays a crucial role in modeling the turbulent stresses and energy dissipation within the flow.
5. Not Applicable to Laminar Flow: In laminar flow, viscous effects dominate, and the concept of turbulent eddy viscosity and mixing length are not applicable because turbulent fluctuations are absent or negligible.