Air flows steadily through a heated pipe as shown below. At the entrance of the pipe the radius is $R_1=0\mathrm{.}01m$ and the density of the air is ${}_1=1\mathrm{.}225k\frac{g}{m^3}.$ The air enters the pipe with a velocity $V_1=3\frac{m}{s}$hat$(e{)}_z$ that is uniform over the cross$-$sectional area. Some ways down the heated pipe, the radius has reduced to $R_2=0\mathrm{.}0075m$ and the density of the air has decreased to ${}_2=1\mathrm{.}0k\frac{g}{m^3}.$ Moreover, the velocity profile at this location is given by the equation

vec$(V{)}_2=V_c(1-\frac{r^2}{R_2^2})hat(e{)}_z$

Where $V_g$ is the velocity at the centerline. For this case determine $V_g.$