Make sure to do a MOMENTUM SHELL BALANCE$-$ DO NOT use Continuity equations

$1.$ There are a number of methods by which one can measure the viscosity of a fluid, a field known as Rheometry, using a device known as a viscometer. One type of viscometer that is commonly used is a parallel$-$disk viscometer $($shown below$).$ In this type of viscometer, the upper disk is spun at an angular velocity of $\backslash$Omega $($s$-1)$ while the bottom disk is held stationary. The surface tension of the fluid keeps it in between the plates during the measurements. While the full development of the velocity profile is a bit beyond what we have done thus far, we can greatly simplify our task by neglecting the variation of the velocity with respect to the radial direction. With this in mind, determine the velocity profile of the fluid between the two plates at some distance R from the center using a shell balance. Be sure to clearly state all assumptions and boundary conditions used in the development of your equation.

$($Hint $1$: Make sure you perform a dimensional analysis on the final equation to ensure that it makes sense$)$

$($Hint $2$: This problem is very similar to the other purely shear flow examples we have discussed several times in class this semester$)$