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

Plot the velocity profile for pipeflow.

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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.

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