Introduction to Fluid Mechanics Overview Picturing Fluids Fluids and Vector Calculus Inviscid Flow and Bernoulli Viscous Flow Boundary Layers Laminar/Turbulent Pipe Flow Pipe Flow Networks Boundary Layers External Flow and Drag Dimensional Analysis/Scaling Compressible Flow

# Laminar / Turbulent Pipe Flow

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5.1 Definition of the Friction Coefficient (02:39)

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

5.2 Laminar flow in a circular pipe (05:12)

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

5.3 Laminar flow, turbulent flow, and mixing (03:03)

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

5.4 Mixing, momentum transport, and eddy viscosity (02:12)

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.

5.5 Roughness (01:18)

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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