Previously, we saw the differential form of mass conservation.
Now let's take a look at the corresponding integral form
of mass conservation.
I'll go back to the channel flow.
And I have flow coming in here and flow going out there.
And I will denote the mass flow rate crossing any surface by m dot.
And for steady flow, we intuitively know that the mass coming in
should be equal to the mass going out, because that
can be no mass accumulation here.
That's with the steady flow assumption.
And if we write that in terms of the mass flow rates,
we can say that the mass flow rate out should be
equal to the mass flow rate coming in.
And that involves the assumption that the flow is steady.
First, let me take a look at the scenario where
I have uniform velocity coming in and uniform velocity going out.
This is the simpler scenario.
And let me also say that the velocity at the inlet and outlet
is perpendicular to the surface.
And then, so the mass flow rate going out
will be equal to density times the velocity
at the outlet, the uniform velocity, times the area of that outlet, which
is going to be this length times some-- I can assume unit distance
perpendicular to the screen.

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- Summer '18