7. For the flow of a thin layer of liquid down an inclined plane shown: a. Using the cross-hatched element and through a force balance, show that the velocity distribution across the layer is: dx y sin 0 и %3 (b² – s² ) Free 2 µ Surface b. Derive an expression for the liquid velocity surface. at the free t dx Y s dx Fixed c. Derive an expression for the discharge per unit width. d. Derive an expression for the shear stress at the fixed wall. Wall

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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7. For the flow of a thin layer of liquid down an inclined plane
shown:
a. Using the cross-hatched element and through a force balance,
velocity
show
that
the
distribution across the layer is:
dx
y sin 0
(b² – s? )
2 µ
u =
Free
Surface
an expression for the
the
b. Derive
t dx
liquid velocity
surface.
at
free
Fixed
Ys dx
c. Derive
discharge per unit width.
d. Derive
an
expression for the
Wall
b
an
expression for the
shear stress at the fixed wall.
Transcribed Image Text:7. For the flow of a thin layer of liquid down an inclined plane shown: a. Using the cross-hatched element and through a force balance, velocity show that the distribution across the layer is: dx y sin 0 (b² – s? ) 2 µ u = Free Surface an expression for the the b. Derive t dx liquid velocity surface. at free Fixed Ys dx c. Derive discharge per unit width. d. Derive an expression for the Wall b an expression for the shear stress at the fixed wall.
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