Problem $2$: Velocity profile

$($time : $20$ minutes$)(20$Marks$)$

The velocity profile for a Non$-$Newtonian fluid has been obtained experimentally and summarized in the next table.

Given the equation of the profile: $,U(r)=U_{\text{a}\text{v}\text{g}}(\frac{3n+1}{n+1})*(1-(\frac{r}{R}{)}^{\frac{n+1}{n}})$

$2-1.$ From the experimental data, give numerical values for R and Umax $!$

$2-2.$ Give the relationship between Umax and Uavg $!($according to the above equation$)$

$2-3.$ Use the above equation and the data table to estimate the value of $(n)!$ What type of fluid is it$?$

$2-4.$ Calculate the average velocity using the relationship obtained in $(3-2)!$

$\backslash$table$[[r(cm),U(\frac{m}{s})$