Mechanical Properties of FluidsNEET Physics · Class 11 · NCERT Chapter 9

Introduction

Fluids — liquids and gases — are everywhere: blood in your arteries, fuel in an engine, air over a wing, water through a pipe. The physics that governs them shows up in NEET as a steady stream of formula-driven problems on Pascal's law, buoyancy, Bernoulli, viscosity and surface tension.

For NEET 2027 expect 1 to 3 questions. Bernoulli's equation, Archimedes, Stokes' law and capillary rise are the heavy hitters. Six formulas in the cheat sheet cover almost every problem.

Pressure in fluids

Pressure is force per unit area perpendicular to the surface:

SI unit: pascal (Pa) = N/m². 1 atm = $1.013\times 10^5\text{Pa}$. In a static fluid, pressure increases with depth:

Here $P_0$ is the pressure at the surface (often atmospheric), $\rho$ is fluid density and $h$ is depth below the surface. Pressure depends on depth, not on the shape of the container.

Pascal's law and the hydraulic press

Pascal's law: pressure applied at any point of a confined incompressible fluid is transmitted equally in all directions, undiminished.

Hydraulic press

Two pistons of areas $A_1$ and $A_2$ are connected by an incompressible fluid. Pressure is the same on both sides:

A small force on a small piston produces a large force on a large piston — the multiplication factor is the ratio of areas. Used in hydraulic lifts, brakes, and presses.

Archimedes' principle and buoyancy

A body fully or partly submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced:

Apparent weight in fluid: $W_{\text{app}}=W_{\text{real}}-F_{\text{buoyant}}$.

Three cases

• Floats: body density ${\rho }_b<{\rho }_f$. Equilibrium with only part of the body submerged.
• Suspended (fully submerged): ${\rho }_b={\rho }_f$. Body stays at any depth.
• Sinks: ${\rho }_b>{\rho }_f$. Body falls to the bottom.

For floating bodies, the fraction submerged equals ${\rho }_b/{\rho }_f$. An iceberg ($\rho \approx 0.92$ g/cm³) shows about 92% submerged in seawater ($\rho \approx 1.025$).

Equation of continuity

For an incompressible fluid in steady flow, the volume flow rate is the same everywhere along a streamline:

Where the pipe is narrower, the fluid moves faster. Pure consequence of mass conservation.

Bernoulli's equation

For steady, non-viscous, incompressible flow along a streamline:

This says pressure energy + kinetic energy + potential energy (all per unit volume) is conserved along a streamline. Rearranged between two points:

Applications of Bernoulli's equation

Speed of efflux (Torricelli's theorem)

Liquid escapes from a small hole at depth $h$ below the free surface of a tank with speed:

Same as a freely falling body — the pressure difference is exactly $\rho gh$.

Venturi meter

Measures flow speed by exploiting the pressure drop across a constriction. From continuity and Bernoulli:

Lift on an aerofoil and Magnus effect

Air moves faster over the curved upper surface of a wing than the flatter lower surface. Bernoulli says faster flow → lower pressure → net upward lift.

Viscosity

Real fluids resist shearing. Newton's law of viscosity for laminar flow:

Here $\eta$ is the coefficient of viscosity (units Pa·s or poise; 1 poise = 0.1 Pa·s) and $dv/dy$ is the velocity gradient perpendicular to flow. Water at 20 °C has $\eta \approx 1\text{cP}=10^{-3}\text{Pa⋅s}$.

Stokes' law and terminal velocity

For a small sphere of radius $r$ moving through a fluid of viscosity $\eta$ at low speed, the viscous drag is:

At terminal velocity, drag + buoyancy balance gravity:

Larger or denser spheres reach higher terminal speeds. More viscous fluids slow them down.

Surface tension and surface energy

Surface molecules have higher PE than interior molecules. The free surface of a liquid behaves like a stretched membrane.

• Surface tension $T$: force per unit length along a line on the surface, perpendicular to the line. Units N/m.
• Surface energy: work needed to increase the surface area by unit amount. Numerically equal to $T$, units J/m².

Excess pressure inside a liquid drop of radius $r$: $\Delta P=2T/r$. Inside a soap bubble (two surfaces): $\Delta P=4T/r$.

Capillary rise

A thin tube dipped in a wetting liquid sees the liquid rise in the tube. Balance of surface tension force and weight gives:

Here $r$ is tube radius, $\theta$ is contact angle (0° for perfect wetting). For non-wetting liquids like mercury ($\theta >90°$, $\cos \theta <0$), the liquid is depressed below the outside level.

Worked NEET problems

Summary cheat sheet

• Pressure with depth: $P=P_0+\rho gh$.
• Pascal's law: $F_2=F_1{A}_2/A_1$ in a hydraulic press.
• Archimedes: $F_{\text{buoy}}=V_{\text{disp}}{\rho }_{f}g$. Fraction submerged = ${\rho }_b/{\rho }_f$.
• Continuity: $A_1{v}_1=A_2{v}_2$.
• Bernoulli: $P+\frac{1}{2}\rho v^2+\rho gh=\text{const}$ along a streamline.
• Speed of efflux: $v=\sqrt{2gh}$.
• Stokes' drag: $F=6\pi \eta rv$.
• Terminal velocity: $v_t=\frac{2r^2({\rho }_s-{\rho }_f)g}{9\eta }$.
• Surface tension: excess pressure in a drop $2T/r$, in a soap bubble $4T/r$.
• Capillary rise: $h=\frac{2T\cos \theta }{\rho gr}$.

Next: try the interactive widgets for hydraulic press, Bernoulli's equation and terminal velocity, or work through the 30+ NEET PYQs with full solutions. To time yourself, take the free 10-question mock test.