Head-pressure valves are in fact the same as pressure-relief valves except they are used upside down. They stay shut until a certain pressure is reached and then open. This way they can keep a fluid head or pressure above the valve and start opening/metering when the fluid head or pressure gets higher. Examples are for instance non-dripping valves in a shampoo dispenser or an anti-bolus valve in an enteral nutrition delivery set.
For this kind of applications one can use