A coating experiment is conducted on a flat photographic film.

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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QUESTION TWO
A coating experiment is conducted on a flat photographic film. The film is pulled away
from a processing bath by rollers at a steady velocity U and inclined angle 0, as shown
in Fig. Q2.
U
Air
Liquid
coating
Moving photo-
graphic film
Fig. Q2: Liquid coating on a photographic film.
As the film leaves the bath, it retains some liquid; and in this experiment, it has reached
the stage where: the velocity of the liquid in contact with the film (i.e., at y =
U. The thickness of the liquid is assumed to be constant at y = 8, and there is no net
liquid flow (as much is being pulled up by the film as is falling back by gravity).
0) is u =
Question 2 continued on next page.
||
Transcribed Image Text:QUESTION TWO A coating experiment is conducted on a flat photographic film. The film is pulled away from a processing bath by rollers at a steady velocity U and inclined angle 0, as shown in Fig. Q2. U Air Liquid coating Moving photo- graphic film Fig. Q2: Liquid coating on a photographic film. As the film leaves the bath, it retains some liquid; and in this experiment, it has reached the stage where: the velocity of the liquid in contact with the film (i.e., at y = U. The thickness of the liquid is assumed to be constant at y = 8, and there is no net liquid flow (as much is being pulled up by the film as is falling back by gravity). 0) is u = Question 2 continued on next page. ||
Question 2 continued.
Conduct the following solving procedures to analyse this flow:
a) Derive an expression for the differential mass balance and simplify it.
b) Derive an expression for the differential momentum balance in the x and y
directions. What are the values of g, and gy as functions of g and 0? Simplify
the format for the momentum equations.
c) From the simplified y -momentum balance, derive an expression for the
pressure p as a function of y, 8, g, and 0. Demonstrate that
əx
= 0.
d) From the simplified x -momentum balance, derive an expression for the liquid
velocity u (as a function of U, y,8 and a, where a = eg sin ở
Assume that the air
exerts a negligible shear stress on the xy -surface of the liquid (Tyx) at y = 8.
e) Derive an expression for the flow rate Q (per unit width, normal to the plane of
Fig. Q2) in terms of U, 8 and a.
f) If there is no net flow, obtain an expression for the film thickness 8 in terms of U
and a.
Transcribed Image Text:Question 2 continued. Conduct the following solving procedures to analyse this flow: a) Derive an expression for the differential mass balance and simplify it. b) Derive an expression for the differential momentum balance in the x and y directions. What are the values of g, and gy as functions of g and 0? Simplify the format for the momentum equations. c) From the simplified y -momentum balance, derive an expression for the pressure p as a function of y, 8, g, and 0. Demonstrate that əx = 0. d) From the simplified x -momentum balance, derive an expression for the liquid velocity u (as a function of U, y,8 and a, where a = eg sin ở Assume that the air exerts a negligible shear stress on the xy -surface of the liquid (Tyx) at y = 8. e) Derive an expression for the flow rate Q (per unit width, normal to the plane of Fig. Q2) in terms of U, 8 and a. f) If there is no net flow, obtain an expression for the film thickness 8 in terms of U and a.
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