Review of physics 2 - Hydromechanics, exercise

Calculate the force $F$ needed for covering by the plug (from the inner site) an opening in the boat. The opening is in depth $h = 3\text{ m}$ under the sea level, the area of the plug is $A = 5\text{ m}^3$, gravity acceleration assume as $g = 10\text{ m}\,\text{s}^{−2}$ and density of water take equal to $\rho_{\text{w}} = 1000\text{ kg}\,\text{m}^{-3}$.

Press machine is made from two connected tubes with two pistons, inside with incompressible fluid (in real case is usually using the hydraulic oil). Lets’ displacements of pistons to be $l_1 = 25\text{ cm}$ and $l_2 = 5\text{ cm}$ respectively and the force acting to the narrower piston is $F_1 = 200\text{ N}$. Calculate force working to the wider piston $F_2$ .

Inside an U-shape tube is mercury and in one of two tubes is the column of water above the mercury, see the picture. Difference between the mercury’s levels is $\Delta h= 2\text{ cm}$. Density of water is $\rho_{\text{w}} = 1000\text{ kg/m}^3$ and density of mercury is $\rho_{\text{m}}=\text{13 600 kg/m}^3$. Gravity acceleration lets’ assume as $g = \text{10 ms}^{−2}$. What is the height of the column of water $h_{\text{w}}$?