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.