Consider the Boltzmann equation,
where
and 
and
are defined in the usual way: 
and
Summing equation (5.23) over i gives
Multiplying by 
before summing gives
Defining, as before,
the fluid momentum through 
we get the same equations as in section 5.1.4.
The equation equivalent to equation (4.60) has an additional
term 
, however, when this is
multiplied by 
and summed over i it
sums to zero by equation (4.39). We therefore obtain the same
expression for 
as we did
in section 5.1.4.
Thus we again obtain the continuity
equation (4.62) in terms of the fluid velocity
and the
Navier-Stokes equation (5.21).
