A viscous incompressible liquid of density p and of dynamic viscosity 7 is carried upwards against gravity with the aid of moving side walls. This laminar flow is steady and fully developed in z-direction and there is no applied pressure gradient. The coordinate is fixed in the midway between the walls as shown below. g=-gk liquid P,n x-d I. The velocity profile in z-direction is pg w(x) = " (x² – d²) + U. 2n II. To be able to carry a net amount of liquid upwards, the wall velocities need to be greater than pgd/(2n). III. If one of the walls stops, increasing the speed of the other wall to 3/2U would carry the same amount of liquid upwards. Which of the above statements are true?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A viscous incompressible liquid of density p and of dynamic viscosity n is
carried upwards against gravity with the aid of moving side walls. This
laminar flow is steady and fully developed in z-direction and there is no
applied pressure gradient. The coordinate is fixed in the midway between
the walls as shown below.
2d
g=-gk
liquid
P, n
x=-d
x=d
I. The velocity profile in z-direction is
pg
w(x) =
(x2 – d) + U.
2n
II. To be able to carry a net amount of liquid upwards, the wall velocities
need to be greater than pgd²/(2n).
III. If one of the walls stops, increasing the speed of the other wall to 3/2U
would carry the same amount of liquid upwards.
Which of the above statements are true?
Transcribed Image Text:A viscous incompressible liquid of density p and of dynamic viscosity n is carried upwards against gravity with the aid of moving side walls. This laminar flow is steady and fully developed in z-direction and there is no applied pressure gradient. The coordinate is fixed in the midway between the walls as shown below. 2d g=-gk liquid P, n x=-d x=d I. The velocity profile in z-direction is pg w(x) = (x2 – d) + U. 2n II. To be able to carry a net amount of liquid upwards, the wall velocities need to be greater than pgd²/(2n). III. If one of the walls stops, increasing the speed of the other wall to 3/2U would carry the same amount of liquid upwards. Which of the above statements are true?
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