Navier stokes equation 유도

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Navier stokes equation 유도

목차

I. Mass conservation
II. Momentum conservation
III. Bernoulli Equation

본문내용

on, Navier-Stokes Bernoulli equation
z
(x,y,z)
x
y
Figure 1. Control volume
I. Mass conservation
For control volume , the accumulation of mass is described as follows:
Accumulation mass inflow mass outflow
of = (x, y, z direction) (x, y, z direction)
mass (kg/s) (kg/s) (kg/s)
=
+
+ ------------------------------ ①
Divide eq ① by and let 0
---------------- ②
If nstant, eq ② becomes
------------- ③
eq ③ is called “continuity”
Integrate eq ② over the entire control volume:
--------------------------------------------------- ④
Uuss-Ostogradskii Divergence theory
Eq ④ becomes
------------------------------------------------- ⑤
For 1 dimension fluid flow
1, v1, A1
2, v2, A2
with steady state condition, eq ⑤ becomes:

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