# Plot the velocity profile for pipeflow. A fluid that flows through a (very long) pipe has zero…

Plot the velocity profile for pipeflow.

A fluid that flows through a (very long) pipe has zero

velocity on the pipe wall and a maximum velocity along the centerline of the

pipe.

The velocity v varies through the pipe cross section

according to the following formula:

where R is the radius of the pipe, β is the pressure

gradient (the force that drives the flow through the pipe), µ0 is a viscosity

coefficient (small for air, larger for water and even larger for toothpaste), n

is a real number reflecting the viscous properties of the fluid (n = 1 for

water and air, n

Make a function that evaluates v(r). Plot v(r) as a function

of r ∈ [0, R],

with R = 1, β = 0.02, µ = 0.02, and n = 0.1. Thereafter, make an animation

of how the v(r) curves varies as n goes from 1 and down to 0.01. Because the

maximum value of v(r) decreases rapidly as n decreases, each curve can be

normalized by its v(0) value such that the maximum value is always unity. Name

of program file: plot_velocity_pipeflow.py.