rupture disk

Are you saying that if you have a 10" line with an opened diversion line of 4" purging fluid and the pressure in the 10" line will go up when purge opens?

Definitely no.

Pressure is inverselly proportional to velocity in full developed flows, when all fluid entering one section of pipe goes out from its same pipe section.

What you have is an increase in the area, with the same pressure feeding the line and a restriction downstream that causes the pressure inside the pipe to build up. At some level, the pressure breaks the disk and you have an increase in the exhaust area (the 4" line), for the same inlet pressure. Pressure then drops, because more fluid is coming out of the pipe.

Its not the same pipe area, will not be the same internal pressure. If you'd like to think this way, the fluid velocity upstream of the diversion will increase due to the smaller flow restriction, so, the pressure will drop. The pressure downstream the diversion will drop as a result.

As the pressure in the downstream piping increases, the velocity/flowrate decreases. When the rupture disk bursts, the pressure in the downstream piping and the 10" pipe dramatically decreases. Because of this decrease in pressure in the 10" pipe, the liquid's velocity/flowrate increases.

Does that make sense to you?

Mike