Beginning with the appropriate form of the Navier€“ Stokes equations, develop an equation in the appropriate coordinate system to describe the velocity of a fluid that is flowing in the annular space as shown in the figure. The fluid is Newtonian, and is flowing in steady, in-compressible, fully developed, laminar flow through an infinitely long vertical round pipe annulus of inner radius R_Iand outer radius R_O. The inner cylinder (shown in the figure as a gray solid) is solid, and the fluid flows between the inner and outer walls as shown in the figure. The center cylinder moves downward in the same direction as the fluid with a velocity v₀. The outside wall of the annulus is stationary. In developing your equation, please state the reason for eliminating any terms in the original equation.

Transcribed Image Text:

Fluid flow around center section Ro