1.State Pascal's Law of fluid pressure.
Sol: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of fluid and vessel walls.
2.State Bernoulli's Principle and write its equation.
Sol: $P + \frac{1}{2}\rho v^2 + \rho g h = \text{Constant}$ along a streamline for an incompressible, non-viscous fluid.
3.State Stokes' Law for viscous force on a sphere.
Sol: $F = 6 \pi \eta r v$.
4.What is surface tension? Write its SI unit and dimensional formula.
Sol: Force per unit length acting normal to imaginary line on liquid surface: $S = \frac{F}{L}$. Unit: $\text{N/m}$, Dimension: $[MT^{-2}]$.
5.Find gauge pressure at depth $10 \text{ m}$ in a lake ($\rho = 1000 \text{ kg/m}^3, g = 9.8 \text{ m/s}^2$).
Sol: $P_g = \rho g h = 1000 \times 9.8 \times 10 = 98000 \text{ Pa} = 98 \text{ kPa}$.
6.Water flows through a horizontal pipe of varying radius. At section 1, $A_1 = 10 \text{ cm}^2, v_1 = 2 \text{ m/s}$. Find velocity at section 2 where $A_2 = 5 \text{ cm}^2$.
Sol: By equation of continuity, $A_1 v_1 = A_2 v_2 \implies 10 \times 2 = 5 \times v_2 \implies v_2 = 4 \text{ m/s}$.
7.Calculate terminal velocity of a raindrop of radius $0.3 \text{ mm}$ falling through air ($\eta = 1.8 \times 10^{-5} \text{ N s/m}^2, \rho_{water} = 1000$).
Sol: $v_t = \frac{2 r^2 \rho g}{9 \eta} = \frac{2 \times (3 \times 10^{-4})^2 \times 1000 \times 9.8}{9 \times 1.8 \times 10^{-5}} \approx 10.89 \text{ m/s}$.
8.Find excess pressure inside a soap bubble of radius $2 \text{ cm}$ ($S = 0.03 \text{ N/m}$).
Sol: $\Delta P = \frac{4S}{R} = \frac{4 \times 0.03}{0.02} = 6 \text{ Pa}$.
