Task $1($of $2)$

Under certain condition, the velocity distribution $u(r)$ of a liquid through the annular pipe are given by:

$u(r)=\frac{G}{4}(R_1^2-r^2)+\frac{G}{4}(R_2^2-R_1^2)\frac{ln(\frac{r}{R_1})}{ln(\frac{R_2}{R_1})},Eq.1$

where $$ is the dynamic viscosity and equal to ${8\mathrm{.}90}^{**}{10}^{-4}P{a}^{**}s$ for water, $R_{\text{I}}$ is the inner cylinder radius,

$R_2$ is the outer cylinder radius, and $r$ is a radial distance from the centerline axis of the pipe. For this

problem, all radii are in units of meters $(m).G(P\frac{a}{m})$ is the normalized gradient pressure per unit length

and is given as:

$G(r)=\frac{r^2}{R_2^2-R_1^2}tan(\frac{r-R_1}{R_2-R_1})$

Write a MATLAB script named HW$4$p$2\_$Taskl$\_$UCusername.m that will prompt the user to enter the

values of $R_1,R_2$ and $r$ as constants. Your script should then make sure the inputted $r$ value is valid: $r>R_{\text{I}}$

and rurtanlnGrr$=0\mathrm{.}35mu=4\mathrm{.}096\frac{m}{s}r.If$ the value $ofris$ valid, your script will then compute and print the values $ofu$ with $3$

decimals and the corresponding units. $If$ the value $ofris$ invalid, your script will print $an$ error message.

You will need $to$ use the MATLAB built$-in$ functions for $tan$ and $lnis$ the Natural Log, you can type $in$

help $logor$ help $tanto$ see how $to$ use these functions. The tangent function $in$ the $G$ equation $isin$

radians.

Sample Test Case:

Enter $R1in$ meters: $0\mathrm{.}2$

Enter $R2in$ meters: $0\mathrm{.}5$

Enter the radial distance, $rin$ meters: $0\mathrm{.}35$

the velocity $atr=0\mathrm{.}35m,isu=4\mathrm{.}096\frac{m}{s}$