How is the Prandtl mixing length defined___________________?
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Answer: C. Zero at the pipe wall
Explanation
Prandtl mixing length represents the average transverse distance traveled by turbulent eddies in shear flow. At the solid pipe wall, fluid velocity is strictly zero due to the no slip condition. Because fluid motion and eddy generation are suppressed at solid boundaries, the mixing length equals zero. Ludwig Prandtl introduced the mixing length hypothesis to model turbulent momentum transfer mathematically. The mixing length increases proportionally with distance away from the solid pipe wall boundary. This semi empirical concept helps bridge the gap between microscopic viscosity and macroscopic turbulence.
Mechanical engineers use mixing length models to predict turbulent velocity profiles in industrial ducts. Environmental researchers apply turbulence models to study pollutant dispersion in atmospheric boundary layers. Advanced computational fluid dynamics software incorporates modified mixing length formulations for closure. Option a is false because mixing length specifically models turbulent flow rather than laminar flow. Option b is incorrect since mixing length varies spatially across the flow field rather than remaining constant. Option d is wrong because option c accurately identifies the zero wall boundary condition.
- Subject
- Engineering
- Category
- Chemical Engineering
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- —
- Difficulty
- medium
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