Expanding Pipe Equation

This depends on some more detail. If the increasing-diameter pipe is capped at the end, the pressure is the same throughout.

If the wide end is open, and air is just flowing through, the pressure will decrease along the length of the pipe, according to pipe friction formulas, which depend on whether the flow is fast enough to be turbulent.

If the flow is supersonic, things can get pretty weird: standing waves, resonances, choked flow, etc. This is a complex topic, on which my further understanding is limited. I doubt that a simple explanation is possible.

thanks for the input.
the wide end is open and air(not pressurized) is blown through it at low speed/velocity. as i understand, higher velocity does not mean higher pressure. will the air pressure still decrease by the time it reaches the wide end?

http://en.wikipedia.org/wiki/Bernoulli%27s_equation

http://en.wikipedia.org/wiki/Discharge_coefficient