Question

What equations are/can be used to describe the velocity profile for a turbulet flow in a pipe and how do you visualise the plot in excel?

Answer 1

The velocity at any point in the cross-section will be proportional to the one-seventh power of the distance from the walls. This may be expressed as follows:

Where u_x is the velocity at a distance y from the walls, u_CL the velocity at the centerline of pipe, and r the radius of the pipe.

This equation is referred to as the Prandtl one-seventh power law.

By using Prandtl one-seventh power law, the mean velocity of flow is found to be equal to 0.817 times the centerline velocity.

note:

Reynold's equation:

where r = density, u = mean velocity, d = diameter and m = viscosity

would help predict the change in flow type. If the value is less than about 2000 then flow is laminar, if greater than 4000 then turbulent and in between these then in the transition zone.

This value is known as the Reynolds number, Re:

Laminar flow: Re < 2000

Transitional flow: 2000 < Re < 4000

Turbulent flow: Re > 4000