By well-mixed, we mean that any substance which enters the control
volume from outside will be essentially instantly distributed evenly
throughout the control volume. This means that the concentration of
the mass we are monitoring inside the control volume should be
identical to the concentration of that mass in our effluent (or
outflow). Let's go ahead and make this assumption, even though it is
not always perfect. Thus,
.
So our equation simplifies from
to the following:
We are now ready to do some final simplifications.