Lecture 33: Hydrodynamics (18 Nov 09)
A. Beginnings
1. FW Sec. 48
2. This is an
ad hoc
approach to the dynamics of a continuous fluid. More
systematic (statistical physics) approach starts from the
N
particle dis
tribution with particleparticle interactions and works to get an equa
tion of motion for the 1body averages. There are a few conservation
laws:
mass, energy, total momentum.
Force terms reflect both the
external forces and the interparticle forces.
3. Text introduces the subject using isotropic simple fluid.
Then for a
small volume boundary by a surface, (1) there is a force/area
≡
P
,
the pressure, (2)
P
is normal,
⊥
the bounding surfaces [i.e., no shear],
and (3)
P
is independent of the orientation of the surface element.
However,
P
may depend on position
r
and then there are gradients of
P
and hence net forces on a volume element.
4. Calculate forces on face
x
of
dV
=
dx
×
dy
×
dz
:
F
x
= [
P
(
x, y, z
)

P
(
x
+
dz, y, z
)]
dydz
’ 
∂P
∂x
dV
5. The acceleration term of a volume element is
d
v
dt
=
∂
v
∂t
+
v
·
~
∇
r
v
where
d/dt
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 Fall '09
 BRUCH
 Physics, Fluid Dynamics, Force, Fundamental physics concepts, volume element, C. Momentum

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