(c) Calculate the wall speed required such that there is no net volume flow of oil either up or down: give your answer for V in terms of the other parameters in the problem, namely, p, H, h, and g. (d) Calculate V for zero volume flow rate for an oil film of thickness 4.12 mm with p = 888 kg/m³ and μ = 0.801 kg/m.s.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Problem 1
Consider steady, incompressible, parallel, laminar flow of a film of oil falling
slowly down an infinite vertical wall which is moving upward at speed V. The
oil film thickness is h, and gravity acts in the negative z-direction (downward).
There is no applied (forced) pressure driving the flow-the oil falls by gravity
alone.
(a) Calculate the velocity fields in the oil film.
(b) Calculate the volume flow rate per unit width of oil falling down the wall
(V/L) as a function of wall speed V and the other parameters in the
problem.
Oil film:
P. μ
P= Patm
Air
(c) Calculate the wall speed required such that there is no net volume flow of oil either up or down: give
your answer for V in terms of the other parameters in the problem, namely, p, u, h, and g.
(d) Calculate V for zero volume flow rate for an oil film of thickness 4.12 mm with p = 888 kg/m³ and μ =
0.801 kg/m.s.
Transcribed Image Text:Problem 1 Consider steady, incompressible, parallel, laminar flow of a film of oil falling slowly down an infinite vertical wall which is moving upward at speed V. The oil film thickness is h, and gravity acts in the negative z-direction (downward). There is no applied (forced) pressure driving the flow-the oil falls by gravity alone. (a) Calculate the velocity fields in the oil film. (b) Calculate the volume flow rate per unit width of oil falling down the wall (V/L) as a function of wall speed V and the other parameters in the problem. Oil film: P. μ P= Patm Air (c) Calculate the wall speed required such that there is no net volume flow of oil either up or down: give your answer for V in terms of the other parameters in the problem, namely, p, u, h, and g. (d) Calculate V for zero volume flow rate for an oil film of thickness 4.12 mm with p = 888 kg/m³ and μ = 0.801 kg/m.s.
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