Question

Fluid in Fig.3B.4. Creeping flow in the re- gion between two stationary con- centric spheres Fluid out 2e 3B.4 Creeping flow between two concentric spheres (Fig. 3B.4). A very viscous Newtonian fluid flows in the space between two concentric spheres, as shown in the fig- ure. It is desired to find the rate of flow in the system as a function of the imposed pressure difference. Neglect end effects and postulate that depends only on r and θ with the other velocity components zero. (a) Using the equation of continuity, show that ve sin θ = u(r), where u(r) is a function of r to be determined (b) write the θ-component of the equation of motion for this system, assuming the flow to be slow enough that the (v . Vv) term is negligible. Show that this gives o- 1뮤.-Ial.)北2)] 0-1a9 (3B4-1) 0B+1, (c) Separate this into two equations r drdr where B is the separation constant, and solve the two equations to get P2-9 (3B.4-4) 2 In cot ε (Pi - P2)R In cot(e/2) 1 (3845) where P, and P2 are the values of the modified θ-ε and θ-π-e, respectively (d) Use the results above to get the mass rate of flow pressure at (3B.4-6) 12x In cot(e/2)

Answer 1

2 Contimuity

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