Answered: Pa Ha 0 Fully developed region b- Film

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Consider a viscous fi lm of liquid draining uniformly down
the side of a vertical rod of radius a , as in Fig. P4.84. At
some distance down the rod the fi lm will approach a terminal
or fully developed draining fl ow of constant outer radius
b , with υ _z = υ _z ( r ), υ _θ = υ _r = 0. Assume that the atmosphere
offers no shear resistance to the fi lm motion. Derive
a differential equation for υ_z , state the proper boundary
conditions, and solve for the fi lm velocity distribution.
How does the fi lm radius b relate to the total fi lm volume
fl ow rate Q ?

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