The Prandtl mixing length is
A. Zero at the pipe wall and is a universal constant
B. Independent of radial distance from the pipe axis
C. Independent of the shear stress
D. Useful for computing laminar flow problems
Answer: Option D
Solution (By Examveda Team)
The Prandtl mixing length is a concept used in turbulence modeling to describe the distance a fluid particle travels before mixing with the surrounding fluid.It is a theoretical construct introduced in the Prandtl’s mixing length theory to estimate turbulent shear stresses.
Near the pipe wall, due to the no-slip condition, the fluid velocity is zero, and so the mixing length is also zero at the wall.
As we move away from the wall, the mixing length increases.
Though the mixing length varies with distance from the wall, it is treated as a universal constant in proportion to distance in certain regions of turbulent flow.
Option B is incorrect because the mixing length is not constant across the radius—it varies.
Option C is incorrect because the mixing length is indirectly related to shear stress through turbulence generation.
Option D is incorrect because the Prandtl mixing length theory is applicable to turbulent flows, not laminar flows.
Hence, the correct interpretation is that the Prandtl mixing length is zero at the pipe wall and is a universal constant in a proportional sense within the turbulent region.
This Question Belongs to Chemical Engineering >> Fluid Mechanics
Join The Discussion
Comments (1)
A. Thermal conductivity
B. Electrical conductivity
C. Specific gravity
D. Electrical resistivity
A. $$\frac{{\text{V}}}{{{{\text{V}}_{\max }}}} = {\left( {\frac{{\text{x}}}{{\text{r}}}} \right)^{\frac{1}{7}}}$$
B. $$\frac{{\text{V}}}{{{{\text{V}}_{\max }}}} = {\left( {\frac{{\text{r}}}{{\text{x}}}} \right)^{\frac{1}{7}}}$$
C. $$\frac{{\text{V}}}{{{{\text{V}}_{\max }}}} = {\left( {{\text{x}} \times {\text{r}}} \right)^{\frac{1}{7}}}$$
D. None of these
A. d
B. $$\frac{1}{{\text{d}}}$$
C. $$\sigma $$
D. $$\frac{l}{\sigma }$$
A. $$\frac{{4\pi {\text{g}}}}{3}$$
B. $$\frac{{0.01\pi {\text{gH}}}}{4}$$
C. $$\frac{{0.01\pi {\text{gH}}}}{8}$$
D. $$\frac{{0.04\pi {\text{gH}}}}{3}$$
The correct answer is: A. Zero at the pipe wall and is a universal constant
---
✅ Explanation:
The Prandtl mixing length (l) is a concept used in turbulent flow modeling (not laminar), particularly in Prandtl’s mixing length theory for eddy viscosity. It represents the average distance a fluid particle moves in the transverse direction before mixing with surrounding fluid.
According to Prandtl:
The mixing length increases with distance from the wall.
It is zero at the pipe wall because there can be no transverse movement at the wall (due to the no-slip condition).
In fully developed turbulent flow, near the wall (in the viscous sublayer), the mixing length varies linearly with distance from the wall:
l = kappa y
Thus, while it is not a universal constant throughout the pipe, it does become zero at the wall, making Option A correct only because of the first part (which is more significant here).
---
Why other options are incorrect:
B. ❌ Mixing length depends on radial distance (or distance from wall).
C. ❌ It is related to shear stress through the velocity gradient.
D. ❌ Mixing length theory is not used for laminar flow (no eddies to model).