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Introduction to Fluid Mechanics

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

3A1 Blank handout

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3A1 5.1 Definition of the Friction Coefficient (02:39)

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

3A1 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

3A1 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.

3A1 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.

3A1 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.

3A1 Completed handout

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