There is no direct calculation that I know of. That is why we use the flow coefficient so as to take into these kinds of effects. If you really need a more accurate pressure drop, I would recommend looking into using vena contracta taps on your flow station. The tough part is that the location of the vena contracta is very dependent on beta ratio and pipe diameter. For smaller pipes, the VC can be very close, if not inside the flanges.
ASME's report on fluid meters has a plot that gives a rough outline of the location of the VC at # of D downstream from the upstream face as a function of beta ratio. This is totally dependent on numerous observations. There is no calculation related. The stated tolerance is ±.2D at β=.2 to ±.5D at β=.75
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