Axial annular flow, equation

As a partial check on the derivations in the conical coordinates, it should be possible to recover two, easily identified, special cases—the radial flow between parallel disks and the axial Poiseuille flow in an cylindrical annular gap. The parallel-disk flow (Section 5.5) is the case where 0 = 0, with x taking the role of r and y taking the role of z. In this case, h = De/2 + x = r. The momentum equations become... 

Helical Annular Flow Consider the helical annular flow between concentric cylinders with an axial pressure gradient and rotating outer cylinder as shown in the accompanying figure. Specify the equations of continuity and motion (z and 6 components) and show that, if a Newtonian fluid is used, the equations can be solved independently, whereas if tj = t](y), where y is the magnitude of y, the equations are coupled. 

Next, the posttorpedo section may be analyzed. The solution to the generalized annular Couette flow problem may be profitably used for wire-coating dies with appropriate modifications to account for the taper in the different sections (i.e., the variation of k with axial distance z). On eliminating A from Eqs. (7) and (10), the following equation for the determination of n, x) is obtained ... 

The flow model was taken from cin unpublished report described In the Appendix. The reactor Is considered to consist of a set of annuli each containing cin equal portion of the volumetric flow. The axial distance Is broken Into subdivisions whose size is dependent upon the stability analysis of the numerical technique. The physical properties at the entrance of each annular section are considered constant in the radial direction. At each axial point, these properties are calculated and the radial coordinate Is resubdlvlded into new annuli. The heat balance is then obtained from the differential equation in cylindrical coordinates transformed Into a difference equation of trldlagonal form which was solved by the method of L.H. Thomas (Reference 6). 

The above analysis was based on the assumption of plug flow of liquid in the z-direction. Schachman (1948) analyzed the same problem using a velocity profile for annular axial flow of the liquid between r and ro- The drag force experienced by the spherical particle was obtained above from Stokes law. For larger particle sizes or higher radial velocities, the resistive radial drag force may be expressed by (see equation (3.1.64))... 

---