State Pascal's Law. A hydraulic lift has piston diameters $5\text{ cm}$ and $30\text{ cm}$. What force on the smaller piston is needed to lift a $1500\text{ kg}$ car?
2.
Derive the variation of fluid pressure with depth $P = P_0 + \rho g h$.
Section B: Bernoulli's Principle & Applications
3.
State Bernoulli's Theorem ($P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$). Derive Torricelli's law for speed of efflux $v = \sqrt{2gh}$.
4.
A Venturimeter is installed in a pipe carrying water ($\rho = 1000\text{ kg/m}^3$). Cross-sectional areas are $A_1 = 20\text{ cm}^2$ and $A_2 = 10\text{ cm}^2$. Pressure head difference is $h = 20\text{ cm}$. Find flow rate.
Section C: Viscosity, Stokes' Law & Surface Tension
5.
State Stokes' Law and derive the formula for terminal velocity $v_t = \frac{2}{9} \frac{r^2 (\rho - \sigma) g}{\eta}$ of a spherical rain drop.
6.
Calculate excess pressure inside a soap bubble of radius $r = 5\text{ mm}$ if surface tension $S = 0.03\text{ N/m}$.
