Introduction to Fluid Mechanics

Laminar / Turbulent Pipe Flow

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The friction coefficient in a pipe is the non-dimensional shear stress.

The velocity profile for laminar flow in a circular pipe is parabolic. In this clip it is derived using large control volumes. (It can also be derived directly from the Navier-Stokes equations). This gives a simple relationship between the friction coefficent, cf, and the Reynolds number, Re. This is cf = 16/Re

At high Reynolds numbers, flows become turbulent. Turbulent flows rapidly mix fluids, while laminar flows do not.

In a turbulent flow, eddies of fluid (little vortices) transport momentum, species, and temperature much more quickly than is possible with molecular diffusion alone. We replace the viscosity with the 'eddy viscosity', which varies througout the fluid.

If a pipe has rough walls, it creates larger eddies in the flow. This increases momentum transport and leads to a higher skin friction coefficient.

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