It's the simple application of
Bernoulli's equation.
Pt = Ps + Pd
-Pt: total pressure
-Ps: static pressure
-Pd: dynamic pressure (1/2 x
density x TAS^2)
The total pressure always remains
constant (in theory) provided no energy is added or taken away. Now if the
streamlines converge, the speed will increase which increases the dynamic
pressure. Applying Bernoulli's equation, the static pressure must decrease for
the total pressure to remain constant.
This equation is only valid for
subsonic incompressible flow. In supersonic flow the results are the opposite,
i.e. in a flow where the streamlines converge the dynamic pressure would
decrease and the static pressure would increase. In supersonic flow you would
apply the Saint Venant's equation which is a little
more complicated than this one.