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Buoy level gauges are level gauges based on Archimedes' law: the dependence of the buoying force acting on the buoy on the level of the liquid. The sensitive element of such level gauges is a massive body (for example, a cylinder) - a buoy suspended vertically inside the vessel and partially immersed in a controlled liquid (Fig. 2).

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Rice. 2. Design scheme of the buoy level gauge

The buoy is mounted on an elastic suspension with stiffness c, acting on the buoy with a certain force (in Fig. 2, such an element is a spring). By increasing the level by H from the zero position 00, we increase the buoy force, which causes the buoy to rise by x, and when it rises, the draft increases, i.e. x < h. This changes the force with which the suspension acts on the buoy, and the change is equal to the change in the buoy force caused by the increase in the draft of the buoy by (h - x):
xc = (h — x)ρ _ggF - (h- x)ρ _ggF,
where c is the stiffness of the suspension; ρ _g, ρ _g is the density of liquid and gas; F is the cross-sectional area of the buoy.
From this it is easy to get an expression for the static characteristic of the buoy level gauge:
x = h/(1 + c(ρ _f - ρ _d)gF).
Thus, the static characteristic of the buoy level gauge is linear, and its sensitivity can be changed by increasing F or reducing the stiffness of the suspension c.
With a large stiffness of the suspension, the buoy will not move, but when the level changes, the force with which it acts on the suspension will change. In this case, with an increase in the level by h, the change in force is equal to hF (ρ _g - ρ _g) g. This principle is used, for example, in buoy level gauges of the types Sapphire-22DU, UB-E, PIUP (formerly UB-P). The latest level gauges are equipped with converters with power compensation (UB-E) with a unified current output signal, UB-P and PIUP with a unified pneumatic output signal).
The diagram of the level gauge with an electric power converter is shown in Fig. 3.

Rice. 3.