Problem #1:
The results from the flow problem of a falling film are only valid for a laminar flow. For the
falling film, this flow regime can only obtained if the Reynolds number, defined by
4
Re
z
u
ρ
δ
μ
=
is smaller or equal 20.
1.
If the film liquid is water at 20
0
C (kinematic viscosity = 0.010037 cm
2
/s), what is the
maximum volume flow rate per unit wall width W.
2.
For Re = 10, and the wall is vertical, calculate the film thickness.
3.
If one wants to choose a different coordinate system as follows: the y and z coordinates are
the same, but the x coordinate is: x = 0 at the solid wall, and
δ
at the gas liquid interface.
Show that the velocity is then given by
2
2
cos
1
2
z
gx
u
ρδ
β
μδ
x
⎡
⎤
⎛⎞ ⎛⎞
=−
⎢
⎥
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
⎢
⎥
⎣
⎦
What is your comment on this choice of coordinate?
Answer:
1. Maximum volume flow rate per unit wall width
The volume flow rate w/
ρ
per unit wall width W is related to Reynolds number as follows
Re
4
w
Q
W
ν
==
To obtain the laminar flow:
Re
=≤
4
20
Q
Thus the maximum volume flow rate for the laminar flow of the falling film
Qc
max
./
20
4
0 050185
2
m
s
2. Film thickness
The film thickness can be calculated from equation of mass flow rate:
where
βρ
=
⎛
⎝
⎜
⎞
⎠
⎟ =
⎛
⎝
⎜
⎞
⎠
⎟
=
33
4
1
9 80665
0 009167
13
2
g
w
Wg
gm
s
cm
cos
cos
Re
cos
,
.
/
.
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 Fall '08
 Peters
 Fluid Dynamics, volume flow rate, uz, τ xz

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