The amount of water having flowed through it is linearly proportional to the absement of the gate, so it is also the same in both cases.

The first published paper on the topic of absement introduced and motivated it as a way to study flow-based musical instruments, such as the hydraulophone, to model empirical observations of some hydraulophones in which obstruction of a water jet for a longer period of time resulted in a buildup in sound level, as water accumulates in a sounding mechanism (reservoir), up to a certain maximum filling point beyond which the sound level reached a maximum, or fell off (along with a slow decay when a water jet was unblocked).

The further the throttle has been opened, and the longer it's been open, the more the vehicle's travelled.PID controllers are controllers that work on a signal that is proportional to a physical quantity (e.g. displacement, proportional to position) and its integral(s) and derivative(s), thusly defining PID in the context of integrals and derivatives of a position of a control element in the Bratland sense[11] depending on the type of sensor inputs, PID controllers can contain gains proportional to position, velocity, acceleration or the time integral of position (absement)…Example of PID controller (Bratland 2014): Strain absement is the time-integral of strain, and is used extensively in mechanical systems and memsprings: Absement originally arose in situations involving valves and fluid flow, for which the opening of a valve was by a long, T-shaped handle, which actually varied in angle rather than position.

[12] In regard to a conjugate variable for absement, the time-integral of momentum, known as momentement, has been proposed.

[13][14][15][16] This is consistent with Jeltsema's 2012 treatment with charge and flux as the base units rather than current and voltage.