The float valve shown in the diagram uses a vertically mounted cylindrical float. The valve used has an effective diameter of $10mm$ and it has to close against a water pressure of $2$ bar gauge. Allow $1\mathrm{.}0N$ for the weight of the float and ignore the weight of the lever arm.

Calculate the depth $\text{'}h\text{'}$ to which the float must be submerged in order to shut off the water flow.

$($All dimensions are in $mm)$