Fluid Mechanics
The hydrodynamic and thermal boundary layers will merge, when

Prandtl number is one
Archimedes number is greater than 10000
Nusselt number tends to infinity
Schmidt number tends to infinity

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Fluid Mechanics
The Prandtl mixing length is

Useful for computing laminar flow problems
Zero at the pipe wall and is a universal constant
Independent of radial distance from the pipe axis
Independent of the shear stress

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