Review of physics 2 - Hydromechanics, exercise
Martin Žáček, dept. of Physics, FEE CTU, zacekm@fel.cvut.cz
Hydrostatics
Opening in the boat:
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 \(\rho_{\text{w}} = 1000\text{ kg}\,\text{m}^{-3}\).
[15 kN]
Press machine:
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 \(F_2\) .
[1 kN]
Mercury in the tube:
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 \(h_{\text{w}}\)?
[27.2 cm]
Opening in the boat:
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 \(\rho_{\text{w}} = 1000\text{ kg}\,\text{m}^{-3}\).
[15 kN]
Press machine:
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 \(F_2\) .
[1 kN]
Mercury in the tube:
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 \(h_{\text{w}}\)?
[27.2 cm]