1.State Pascal's Law and explain the working principle of a Hydraulic Lift.
Sol: Pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid: $P = \frac{F_1}{A_1} = \frac{F_2}{A_2} \implies F_2 = F_1 \left(\frac{A_2}{A_1}\right)$.
2.State Bernoulli's Principle and write its equation for streamline flow of an incompressible non-viscous liquid.
Sol: Total energy per unit volume is conserved along a streamline: $P + \frac{1}{2}\rho v^2 + \rho g h = \text{Constant}$.
3.State Stokes' Law for terminal velocity of a small sphere falling through a viscous medium.
Sol: Viscous drag $F_v = 6\pi \eta r v$. Terminal velocity $v_t = \frac{2 r^2 (\rho - \sigma) g}{9 \eta}$.
4.Derive the height of capillary rise formula $h = \frac{2S \cos\theta}{r \rho g}$.
Sol: Upward surface tension force $2\pi r S \cos\theta = \text{Weight of liquid column} = \pi r^2 h \rho g \implies h = \frac{2S \cos\theta}{r \rho g}$.
