Flow through an annulus

The volumetric flow rate Q for laminar flow through an annulus of length L with outer and inner diameters D and d is given by [2] 

It can be shown that for a very narrow annular gap d - D in the annulus this equation reduces to the wide-slot formula above. 

4 A rod being pushed into a cup filled with liquid 

The viscosity 77 of a very viscous liquid such as glucose s)U up can be calculated from the force F needed to push a rod of radius Ui centrally into a cup of radius Ui at a velocity V as 

The rate of change of the separation h with respect to time t is given by 

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Figure 5.15 Schematic diagram of pressure flow through an annulus.

Derive an expression for the Nusselt number in fully developed laminar slug flow through an annulus when the inner and outer surfaces of the annulus have diameters of Dj and D0 respectively and when there is a uniform heat flux applied at the inner surface and when the outer surface is adiabatic. 

Some simple heal transfer equipments consist of two concentric tubes, and are properly called double-tube heat exchangers (Fig. 8-27). In such devices, one fluid flows through the tube while the other flows through the aunular space. The governing differential equations for both flow.s are identical. I herefore, steady laminar flow through an annulus can he studied analytically by using suitable boundary conditions. 

The simple hydraulic-radius rule does not apply to laminar flow through noncircular sections. For laminar flow through an annulus, for example, / and Nrc are related by the equation ... 

A. W. Bennett and H. A. Kearsey, Heat Transfer and Pressure Drop for Superheated Steam Flowing Through an Annulus With One Roughened Surface, Atomic Energy Research Establishment 4350, AERE, Harwell, UK, 1964. 

Likewise, the cold legs connect the PCUs at the elevation of the compressor outlets. Flow is collected from the compressor diffuser, and approximately 90% of the flow at 140°C crosses in the cold leg and enters the top of an annular ring of coolers to flow downward, to be cooled, and then to go directly into the next compressor inlet. Approximately 10% of the cold flow is b3 assed upward to flow through an annulus around the hot-leg duct, so the hot-leg pressure boundary is maintained at the same temperature as the cold-leg boundary to minimize thermal stresses due to the PCU vessels being connected at two elevations by cross-over legs. The cold cross-over leg eliminates the vessel volume and pressure drop that... 

Huang, C.L., 1974. Applying quasi-linearization to the problem of flow through an annulus with porous walls of different permeability. Appl. Sci. Res. 29, 145-158. 

The radial dependence of may be obtained from standard solutions of flow through an annulus (Bird et al, 1960) ... 

FIGURE 2.9 The function F s, k) needed for obtaining the volume rate of flow through an annulus for a power-law fluid. 

B.4 Adapting the Parallel Plate Solution to Annular Flow. For small annular gaps (e.g., k = 0.9) the expression for Q for flow through a slit of a power-law fluid (Problem 2B.3) ean be used to obtain an expression for Q for annular flow. Adapt the parallel plate flow solution for the power-law model to that for flow through an annulus with a small gap (you should obtain the expression in Eq. 2.103). 

B.7 Flow Through an Annulus with a Rotating Mandrel. In some processes involving pressure-driven flow of polymer melts through an annulus the outer or inner cylinder (mandrel) is rotated as shown in Figure 2.19. 

C.4 Velocity Maximum in Annular Flow for Noninteger Values of the Power-Law Index. Equation 2.39 is used to find the position of the maximum in the velocity field for flow through an annulus. For n = 0.59 and k = 0.5 and 0.8, determine ft using the IMSL numerical integration subroutine QDAGs described in Appendix D.5 or quad in MATLAB. 

B.8 Multiple Layer Flow Through an Annulus. Obtain expressions for and and for finding a similar... 

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