Not sure what you are referring to. The foot vent, historically, has been a connection from the base of a stack into the vent stack to relieve the pressure build up in a tall building. The intermediate connections, on the upper floors, are called relief vents. Bar sinks are often drained to a floor sink using a raised open connection, with no traps at the sink. When they are installed that way, they do not need a vent, unless the local authority requires them on lateral drains exceeding a certain length.