Question: consider the incompressible fluid flow of a newtonian fluid shown...
Consider the incompressible fluid flow of a Newtonian fluid shown in the Figure. In Chapter 8 of the Welty, Rorrer and Foster book, the authors carry out a momentum balance around the differential element shown in the Figure (a shell balance), and obtain a parabolic velocity profile for this system:
v𝑥 = −(dP/𝑑𝑥) R^2/4𝜇 [1−(r/𝑅)^2 ]
Show that you can obtain the same result, starting with the appropriate form of the Navier-Stokes equations combined with the continuity equation. Tip: use a cylindrical coordinate system (so x shown in the figure becomes z). Sketch the velocity profile and indicate the point of maximum velocity.