The purpose of this problem is for you to see how the series solution for the above problem

converges, how the different terms in the sum contribute, etc. Another purpose is for you to see

how the velocity profile develops from that of equation $4\mathrm{.}1-15($solution for flow over a moving

plate in a semiinfinite fluid $-$ at small times when the penetration depth is smaller than b$)$ to the

linear steady state profile for flow between two plat plates where the lower plate is moving.

You will need to think about how many terms you need to include in the sum.

Write a Matlab or Python code and plot the dimensionless velocity profile in problem $4$ as a

function of dimensionless distance between the plates $(),$ for $=0,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}5,1,2,.$ Your

plot should be like Figure $4$D$.2$ with $=\frac{v_x}{v_o}$ plotted versus $=\frac{y}{b}$ for different values of

$.($The profiles will not look like those on Figure $4$D$.2$ though.$)$