An incompressible Newtonian fluid is flowing through an annular region as shown

Question

An incompressible Newtonian fluid is flowing through an annular region as shown in the figure. Assuming that the flow is steady and laminar and that the gravity is negligible, we want to determine the velocity profile by solving the equations of motion along with appropriate boundary conditions.

Considering the annular geometry of the flow, the cylindrical coordinate system must be the obvious choice. When the cylindrical core with radius ri is concentric with the tube of inner radius ro, the laminar flow must be axisymmetric (i.e., independent of theta ?), and the radial and the circumferential components of the velocity vector must be zero.

That is, u = (ur, u?, uz) = (0, 0, uz).

(a) What does the continuity equation indicate?

(b) Write down the r-,?- and z-directional momentum equations showing only non-zero terms.

(c) What are the boundary conditions for this flow?

(d) Solve the equations in (b) using the boundary conditions in (c) to determine uz.

(e) Using the solution in (d), derive an expression for the volumetric flow rate.

(f) Determine the radial position r = rm where the velocity is maximum.

Explanation / Answer

http://www.pearsonhighered.com/samplechapter/0137398972.pdf
pg 291 within the pdf solves the equation for boundary conditions and how to do the volumetric flow rate. It doesn't have all the steps but it shows how to do it sort of generally

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.