Practice Problems on Conservation of Mass
C. Wassgren, Purdue University
Page 1 of 23
Last Updated:
2010 Sep 08
COM_01
Construct from first principles an equation for the conservation of mass governing the planar flow (in the
xy
plane)
of a compressible liquid lying on a flat horizontal plane.
The depth,
h
(
x
,
t
), is a function of position,
x
, and time,
t
.
Assume that the velocity of the fluid in the positive
x
-direction,
u
(
x
,
t
), is independent of
y
.
Also assume that the
wavelength of the wave is much greater than the wave amplitude so that the horizontal velocities are much greater
than the vertical velocities.
Answer(s):
0
h
uh
t
x
If incompressible:
0
h
uh
t
x
x
y
h
(
x,t
)
u
(
x,t
)
free surface
liquid

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