Bonus: Do you know the book this question comes from?

Various manufacturing processes require that a thin, uniform coating of a liquid be created on a solid substrate. This may be done by applying a certain amount of the liquid on top of the substrate and then spinning it rapidly. As shown in Emslie et al. (1958), such liquid films level quickly, after which they gradually thin. This allows the fluid dynamics during most of the coating step to be modeled as in Fig. P7-28. Spinning the substrate at an angular velocity causes the liquid to flow outward, thinning the film as its thickness h(t) remains uniform. (a) Assuming that v=r, it has been proposed that the r-momentum equation be reduced to z22vr=2r a. Using the r-component of the Navier-Stokes equation as stated in the problem find the general solution for vr(r,z). What are the boundary conditions? Use them to solve for the integration constants. Which term contains the time dependance? b. Calculate flow rate q where q=[ area/time ] c. Determine an expression for the deposition rate as a function of h using the initial condition h(t=0)=h0