You would probably have to narrow down your question to get a sensible answer, as a 'relief valve' cover a fairly vast area of valves and applications. The reason for the bypass would also have to be defined:
I can think of at least one example:
If you start with a pressure reduction station in a water supplying net, you would ideally have pressure reduction valve with filter in front, isolating valves upstream and downstream, and a bypass string of all, with a manual throtteling valve, to secure water supply downstream at downtime of the reduction valve.
The pressure reduction valve station would ideally have the same layout if you replace the pressure reduction valve with an overpressure control valve, keeping the upstream pressure constant within a certain limit.
In this case the bypass would have to be designed to give sufficient outlet (defined by max inlet) to avoid overpressure.
In all cases I can think of (you have also some similar systems within hydro-elecrical stations regulating outlet by turbine downtime) the bypass is a 'doubling up' of automatic or driven valves, with a simpler, cheaper 'extra' line for safety reasons, mostly with manual regulation.
Dimensioning: sufficient to give flow of necessary amount for the downtime periode.
One special application: If you have a safety relief valve with a bursting disc upstream, you could also have a smaller manual 'bypass' connected to the pipeline between the disc and PSV, just to check the pressure here to ensure the bursting disc is not leaking.
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