Question: 

Why effective diameter formula is different in operating and hydrotest condition tube side compared to hydrotest condition shell side?

Answer: 

In operating and hydrotest condition (tube side) cases the end brackets (Front End & Rear End) will be connected to the tubesheet. Hence taking the bolting loads, bracket weights and external loads while performing the calculation. Hence effective diameter De = (Ds+Gc)/2, Where Ds = Inside shell diameter & Gc = Channel gasket load diameter

Whereas, In hydrotest condition (shell side) case the end brackets (Front End & Rear End) are not present. Hence not taking any effect of bolting loads, bracket weights and external loads while performing the calculation.

Hence effective diameter De = Ds