Working principle of tank roof breathing manholes

The OP is referring to the breather valve on top of the tank, right? I’ve never seen a breathing manhole; I’ve only seen lighting holes and vent holes. Below is an explanation of how respirator valves work, found online. Hopefully, this is what the original poster was looking for. Principle of operation of a breather valve: The breather valve operates by using a spring to position the valve plate; whether it allows exhalation or inhalation depends on the positive or negative pressure. A breather valve should be capable of relieving both positive and negative pressures. Specifically, when the container is subjected to positive pressure, the breather valve opens to allow gases to escape, thereby releasing the excess pressure ； When the container is subjected to negative pressure, the breather valve opens to allow gas to be drawn in and relieve the negative pressure. This ensures that the pressure remains within a certain range, guaranteeing the safety of the container. There are two types of breather valves: one allows exhalation or inhalation when a certain pressure is reached; the other is designed to allow only exhalation and no inhalation. This can be understood as using two one-way valves with appropriate pressure settings in place of each other. Breather valves not only help maintain pressure equilibrium within storage tanks and prevent them from rupturing under overpressure or vacuum conditions, but also help reduce medium loss within the tanks. Steam traps serve to prevent steam leakage and drain condensate in steam heating systems. Selecting the appropriate steam trap ensures that steam heating equipment operates at maximum efficiency. To achieve the optimal results, it is necessary to have a comprehensive understanding of the operating performance and characteristics of various types of breathing valves. There are many types of breather valves, such as all-weather breather valves, explosion-proof and flame-arresting breather valves, all-weather freeze- and fire-resistant breather valves, jacketed insulated breather valves, freeze-resistant breather valves, double-nozzle breather valves, breather valves with an exhaust outlet, breather valves with dual outlets, all-weather quick-opening breather valves, safety breather valves, and flame-arresting single-suction valves.

He was referring to the breather valve on the can

It’s just that a breather valve is attached to the top or side of the manhole flange, right? Have seen drawings of such horizontal storage tanks~