Consider a tank filled with $3$ immiscible liquid $A$, $B$ and $C$ at static equilibrium, as shown in the figure. At $2 \: cm$ below the liquid $A$- liquid $B$ interface, a tube is connected from the side of the tank. Both the tank and the tube are open to the atmosphere.

At the operating temperature and pressure, the specific gravities of liquids $A$, $B$ and $C$ are $1,2$ and $4$, respectively. Neglect any surface tension effects in the calculations. The length of the tube $L$ that is wetted by liquid $B$ is _______ $\text{cm}$