Mechanical Properties of Fluids

Fluids are substances that have the ability to flow, primarily liquids and gases. The capacity to flow is one of the most important features of fluids that distinguishes them from solids, liquids, and gases as a whole. Solids have a definite shape and volume, whereas fluids do not and take the volume of the container they are housed in. Pressure, Pascal's law, streamlined flow, Bernoulli's principle, and several sub-topics fall under this class 11 NCERT chapter Mechanical Properties of Fluids.

This chapter explains how fluids behave, including concepts like pressure, buoyancy, viscosity, surface tension, and flow. Students will learn the important formulas, derivations, and real-life applications of these concepts. Understanding this chapter helps in solving numerical and conceptual problems for annual exams. This Chapter is very important for competitive exams like JEE and NEET.

Mechanical Properties of Fluids

Main topics discussed in mechanical properties of fluids class 11 notes are:

1. Introduction

Liquids and gases are called fluids because they can flow, unlike solids. Fluids have no fixed shape; liquids have fixed volume, while gases fill the entire container. Solids and liquids are almost incompressible, but gases are highly compressible. A key property of fluids is that they offer very little resistance to shear stress, unlike solids.

2. Pressure

Pressure ( $\mathbf{P}$ ) is the force applied per unit area on a surface, acting perpendicular to it.

$
P=\frac{F}{A}
$

Sl unit: Pascal (Pa) $=1 N / m^2$.
Pressure is a scalar quantity.

• Pascals Law
• Variation of Pressure with Depth
• Unit of Pressure

3. Streamline Flow

Streamline flow (or laminar flow) is the type of fluid motion in which every particle of the fluid follows a smooth path, and paths of nearby particles do not cross each other.

The velocity of particles at a point remains constant with time.

Streamlines are tangent to the velocity vector of the fluid at every point.

Equation of Continuity (Consequence of Streamline Flow)

In streamline flow, the mass of fluid passing through a tube of flow is conserved.
For a pipe of varying cross-section:

$
A_1 v_1=A_2 v_2
$

Where:
$A_1, A_2=$ cross-sectional areas
$v_1, v_2=$ fluid velocities

• Streamline Flow

4. Bernoulli’s Principle

In 1738, a Swiss scientist, Daniel Bernoulli, gave an important relation between the pressure, velocity, and height of a moving fluid. This is known as Bernoulli’s principle.
It is based on the law of conservation of energy and applies to fluids in streamline flow.

Statement
For an incompressible, non-viscous fluid in a steady flow, the sum of the pressure energy, kinetic energy and potential energy per unit volume remains constant at every point of the streamline.

$
P+\frac{1}{2} \rho v^2+\rho g h=\text { constant }
$

Where,
$P=$ pressure of the fluid
$\rho=$ density of the fluid
$v=$ speed of the fluid
$h=$ height above the reference level

• Bernoulli’s Principle

5. Viscosity

Definition:
Viscosity is the property of a fluid by virtue of which it resists the relative motion between its different layers. It is due to internal friction between fluid layers.

Formula:
If two layers of area $A$, separated by distance $d x$, have velocity difference $d v$, then the tangential force is:

$
F=\eta A \frac{d v}{d x}
$
Here, $\eta$ is the coefficient of viscosity.

Stokes' Law:
Viscous force on a sphere of radius $r$ moving with velocity $v$ :

$
F=6 \pi \eta r v
$

Terminal Velocity:

$v_t=\frac{2}{9} \frac{r^2(\rho-\sigma) g}{\eta}$

• Viscosity
• Stokes' law & Terminal Velocity

6. Surface Tension

Definition
Surface tension is the property of a liquid surface due to which it behaves like a stretched elastic membrane, trying to have minimum surface area.

It is defined as:
The force per unit length acting along the surface of a liquid at rest, perpendicular to an imaginary line drawn on the surface.

Formula

$
T=\frac{F}{l}
$

Where,
$T=$ surface tension
$F=$ force acting along the surface
$l=$ length on which the force acts

Angle of Contact
The angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid is called angle of contact ( $\boldsymbol{\theta}$ ).
Wetting: $\theta<90^{\circ}$ (e.g., water on glass).
Non-wetting: $\theta>90^{\circ}$ (e.g., mercury on glass).

Capillary Rise/Depression
Due to surface tension, liquids rise or fall in a narrow tube.

$
h=\frac{2 T \cos \theta}{\rho g r}
$
Where $h=$ rise/fall, $r=$ radius of tube.

• Surface Tension
• Surface Energy