To keep the velocity in the inlet header at the same 9.84 ft/sec inlet velocity to the three pumps you need a 13.86 inch ID header if the 8-inch pump inlet diameter is in fact the ID and not the OD of the piping. The magical equation is Velocity =Flow/Area. Don't you have a calculator and a set of conversion factors?
For me the issue is not velocity but pressure distribution. I would select the header sizes so that irrespective of the pump combinations in service each pump had the substantialy same flow