What is the formula for pressure at depth h in a fluid of density ρ?

P = P₀ + ρgh, where P₀ is atmospheric pressure.

State Pascal’s Law and its application in hydraulics.

A change in pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid. Application: Hydraulic lifts.

What is the relation between absolute pressure, gauge pressure, and atmospheric pressure?

P_absolute = P_gauge + P_atmospheric.

State Archimedes’ Principle.

A body immersed in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid:
FB = Vρg

What is the equation of continuity in fluid dynamics?

A₁  v₁ = A₂ v₂ (Product of cross-sectional area and velocity is constant).

Write down Bernoulli’s equation and its significance.

P + 1/2ρv² + ρgh = constant.
Significance: It expresses the conservation of energy in fluid motion.

Derive the velocity of efflux from a small hole at depth h in a tank.

(same as a freely falling body).

Explain the Venturi effect and write its equation.

When fluid flows through a constricted section, velocity increases, and pressure decreases:

What is the relation between surface tension and excess pressure inside a liquid drop?

P_excess = 2T/r (for liquid drop),
P_excess = 4T/r   (for soap bubble).

What is the formula for the height of liquid rise in a capillary tube?

Write down Stoke’s law for the viscous force on a sphere falling in a fluid.

F=6πηrv,
where η is the viscosity of the fluid.

Define Reynold’s number (Re) and its significance.

• Re < 2000 → Laminar flow
• 2000 < Re < 3000  → Transitional flow
• Re>3000 → Turbulent flow

Write Poiseuille’s equation for flow rate in a pipe.

What is the work required to break a big drop into n small drops?

W = 4πR²T(n^1/3−1).

What determines the stability of a floating body?

The Metacenter (M) should be above the center of gravity (G) for stability.