b) Consider a steady, incompressible, parallel, laminar flow of a film of oil falling slowly down a flat vertical wall as depicted in Figure Q2(b). Oil film P = Patm Fixed wall h- Figure Q2(b) Given the pressure does not change for the surrounding air and oil film, i) state all assumptions you require to simplify the above to a one-dimensional flow problem. i) write the continuity equation and reduce the 3-dimensional Navier-Stokes equation problem. based on the above assumptions to a one-dimensional flow ili) find the vertical (z-direction) velocity profile using non-slip boundary condition at the wall and negligible shear at the free surface. 160

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Question
b)
Consider a steady, incompressible, parallel, laminar flow of a film of oil falling slowly
down a flat vertical wall as depicted in Figure Q2(b).
Oil film
P= Patm
Fixed
wall
Figure Q2(b)
Given the pressure does not change for the surrounding air and oil film,
i)
state all assumptions you require to simplify the above to a one-dimensional
flow problem.
ii)
write the continuity equation and reduce the 3-dimensional Navier-Stokes
equation
problem.
based on the above assumptions to a one-dimensional flow
ii)
find the vertical (z-direction) velocity profile using non-slip boundary condition
at the wall and negligible shear at the free surface.
160
Transcribed Image Text:b) Consider a steady, incompressible, parallel, laminar flow of a film of oil falling slowly down a flat vertical wall as depicted in Figure Q2(b). Oil film P= Patm Fixed wall Figure Q2(b) Given the pressure does not change for the surrounding air and oil film, i) state all assumptions you require to simplify the above to a one-dimensional flow problem. ii) write the continuity equation and reduce the 3-dimensional Navier-Stokes equation problem. based on the above assumptions to a one-dimensional flow ii) find the vertical (z-direction) velocity profile using non-slip boundary condition at the wall and negligible shear at the free surface. 160
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