Why straight run are required for installation of Orifice?

The orifice pressure difference is affected by flow swirl and a flow profile which is different from the research flow data.

The only way to get accurate data is to replicate, as best as possible, the same flow patterns as were to develop the data. It is far easier to reproduce straight runs than the various possible not-straight.

Note that the equations for flow through an orifice plate show a correction factor from the theoretical of about 0.60.

The difference is in the chaotic flow pattern as the fluid is gathered to the center to go through the orifice and then as it expands downstream. Much of the differential is recovered as the fluid slows and some of the kinetic energy is converted back to pressure.