NEET Physics: Waves – NCERT Masterclass & 100 MCQ Quiz

MECHANICAL PROPERTIES OF FLUIDS

Complete NCERT Study Notes & 5-Part Mega Quiz for NEET

1. Pressure and Pascal's Law

A fluid (liquid or gas) exerts pressure equally in all directions. Pressure $P = \frac{F}{A}$. At a depth $h$ inside a liquid of density $\rho$, the absolute pressure is:

$$P = P_a + \rho g h$$

Pascal's Law: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This is the working principle of the Hydraulic Lift ($\frac{F_1}{A_1} = \frac{F_2}{A_2}$).

2. Fluid Dynamics & Equation of Continuity

For the steady (streamline) flow of an incompressible, non-viscous fluid, the mass crossing any section of the pipe per second remains constant.

$$A_1 v_1 = A_2 v_2$$

Where $A$ is the area of cross-section and $v$ is the fluid velocity. Thus, fluids flow faster through narrower sections.

3. Bernoulli's Principle

Based on the law of conservation of energy, for a steady flow of an ideal fluid, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant.

Bernoulli's Equation:
$$P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}$$

Applications: Venturimeter, atomizer, dynamic lift on an aeroplane wing, and blowing off of roofs during wind storms.

4. Viscosity and Stokes' Law

Viscosity is the internal friction of a fluid. The viscous drag force $F$ between two fluid layers is given by Newton's formula: $F = -\eta A \frac{dv}{dx}$, where $\eta$ is the coefficient of viscosity.

Stokes' Law: The backward viscous force acting on a small spherical body of radius $r$ falling with velocity $v$ through a fluid is $F = 6\pi\eta rv$.

Terminal Velocity: When the viscous drag and buoyant force balance the weight, the body falls with a constant velocity: $v_t = \frac{2r^2(\rho - \sigma)g}{9\eta}$.

5. Surface Tension and Capillarity

Surface Tension ($S$): The property of a liquid surface to behave like a stretched elastic membrane. $S = \frac{\text{Force}}{\text{Length}}$ or $S = \frac{\text{Surface Energy}}{\text{Area}}$.

• Excess Pressure inside a liquid drop: $P = \frac{2S}{R}$
• Excess Pressure inside a soap bubble: $P = \frac{4S}{R}$

Capillary Ascent Formula: The height $h$ to which a liquid rises in a capillary tube of radius $r$ is:

$$h = \frac{2S \cos\theta}{r \rho g}$$

Where $\theta$ is the angle of contact.

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🚀 NEET FLUID MECHANICS MEGA QUIZ (100 MCQ)

Solve the 5 parts below to master Pressure, Bernoulli's, Viscosity, and Surface Tension.

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