$$P = \frac{F}{A} \quad (\text{Pa} = \text{N/m}^2) \qquad \text{Liquid pressure } P = \rho g h$$

• Total pressure at depth $h$: $P_{\text{total}} = P_{\text{atm}} + \rho g h$. Atmospheric pressure $\approx 1.01\times10^5$ Pa ($760$ mm Hg).
• Pressure in a liquid acts equally in all directions; it depends only on depth and density.

Hydraulic machine (Pascal's principle)

$$\frac{F_1}{A_1} = \frac{F_2}{A_2} \qquad \text{MA} = \frac{F_2}{F_1} = \frac{A_2}{A_1}$$

Upthrust (Archimedes' principle)

$$\text{Upthrust} = \text{weight of fluid displaced} = \rho_{\text{fluid}}\, g\, V_{\text{displaced}}$$ $$\text{Apparent weight} = \text{real weight} - \text{upthrust}$$

• Floating: upthrust $=$ weight of the body. Fraction submerged $= \dfrac{\rho_{\text{body}}}{\rho_{\text{liquid}}}$.

Gas laws (temperature in kelvin)

$$\text{Boyle (constant } T\text{): } P_1V_1 = P_2V_2$$ $$\text{Charles (constant } P\text{): } \frac{V_1}{T_1} = \frac{V_2}{T_2} \qquad \text{Pressure law (constant } V\text{): } \frac{P_1}{T_1} = \frac{P_2}{T_2}$$ $$\text{General gas law: } \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$ $$T(\text{K}) = \theta(^\circ\text{C}) + 273$$