The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

If you are provided with a glass of water and an apple, you can easily distinguish between their properties by looking at them. Water is not rigid, whereas apples are. Water is less dense compared to apples. Liquids and gases are the states of matter which can flow; hence they are called **fluids**.

If you want to cut a fruit with a knife, you will always use a sharp knife, rather than a blunt one. Do you know why the foundations of buildings are always wide? The reason behind both situations is force and its coverage area. If the area is less, more pressure can be applied even with the same force. The above-mentioned examples act as the **application of pressure** in our day-to-day life.

If the force acts on a smaller area, it has a greater impact. This is known as **pressure**. Try to immerse a bottle in water. You will observe some sort of upward force from the water on the bottle. This happens because when an object is submerged in a fluid at rest, the fluid exerts a force on its surface. The force exerted by the fluid at rest is perpendicular to the surface in contact with it.

Pressure can be defined as the normal force acting per unit area on the object. So,

With the formula given below, pressure in a limiting sense could be found.

The density of the fluid depends upon mass of the fluid and volume of the fluid. The formula is:

Blaise Pascal observed that when a fluid is at rest, its pressure is the same at all the points if height remains the same. The diagram given below demonstrates **Pascal’s law**.

An element ABC-DEF is present inside the fluid at rest. Pa, Pb, and Pc are the pressures exerted on the object corresponding to the normal forces Fa, Fb, and Fc.

The equation given by **Pascal’s law** is:

Applications of **Pascal’s law** include devices such as hydraulic lift and hydraulic brakes.

**Streamline flow** is taken into account while studying fluid dynamics. Fluid dynamics is the term used for the study of the fluids in motion. You might have seen that when you turn on a tap slowly, the water flows smoothly but becomes less smooth when the speed of the outflow is increased.

Flow of the fluid can be said to be steady when at any given point, the velocity of each particle of the fluid particle remains constant in time.

(a) A typical trajectory of a fluid particle

(b) A region of **streamline flow**

Steady flow or **streamline flow** is achieved at low speed of the fluid. This flow becomes** turbulent **i.e., loses steadiness beyond a critical speed. This is also termed **tube flow**. You might have observed small foamy whirlpool-like regions (white water rapids) when a fast-flowing stream strikes a rock.

Let’s imagine that fluid is moving in a pipe of varying cross-sectional area. Now keep the pipe at varying heights. Suppose that an incompressible fluid is flowing through the pipe with a steady flow. Its velocity must change, and force is required to produce this acceleration, which is caused by the fluid surrounding it. According to **Bernoulli’s principle**, the pressure must be different in different regions.

**Bernoulli’s equation relates** to the pressure difference between two points in a pipe to velocity changes (kinetic energy) and elevation changes (potential energy).

ρ = Density of the fluid

h1 and h2 = heights

v2 and v1 = velocities

Δm = ρA1v1 Δt = ρΔV; mass passing through the pipe in time Δt,

Thus,

Change in potential energy; ΔU = ρgΔV (h2 −h1) (since U = mgh)

Change in kinetic energy; ΔK = ρΔV ( v22 −v12 ) (since K=½ mv2)

**Bernoulli’s equation**:

P= Sum of pressure in streamline flow

½ ρv2 = Kinetic energy

ρgh = Potential energy

Take a spoonful of honey and that of fruit juice and slowly pour it into an empty vessel. You will observe that honey drops slowly from the spoon as compared to fruit juice. This resistance to fluid motion is called **viscosity**.

There is some force between the layers of the fluid. This type of flow is known as **laminar**. The layers of liquid slide over one another. When a fluid flows in a pipe or a tube, then along the axis of the tube velocity of the liquid layer is maximum. This velocity decreases gradually as we move towards the walls, where it becomes zero. Such a type of flow in a tube is called **tubular flow**.

For the fluid, we consider shear strain that is Δ*x*/*l*.

Viscosity of a fluid is defined as the ratio of shearing stress to the strain rate.

*F*/*A* = Stress rate

*v*/*l* = Strain rate

The viscosity of different fluids depends upon stress and strain rate. With the increase in temperature, **the viscosity** of the liquids decreases.

You must have noticed that oil and water never mix, and mercury does not wet glass but water sticks to it. This is associated with the free surface of liquids.

These surfaces of the fluids possess some additional energy. This phenomenon is known as **surface tension**.

Molecules of liquid stay together because of the attraction between them. Molecules on a liquid surface have some extra energy as compared to molecules present inside it. Thus, liquids tend to have the least surface area. The increased surface area requires energy.

One of the examples of **surface tension** is that free liquid drops and bubbles are spherical.

**Q1. What are the 4 properties of fluids?**

**A1**. Properties of fluids are buoyancy, density, pressure, viscosity, and surface tension.

**Q2. What are the properties of all fluids?**

**A2**. 4 properties of all the fluids are:

- Fluids don’t have fixed volume and shape; hence they are not rigid.
- They have a lesser density than solids.
- Intermolecular space between the particles is very less in fluids.
- Fluids are highly compressible in nature.

**Q3. How is the viscosity of the fluids affected by temperature?**

**A3**. The viscosity of liquids decreases with temperature.

**Q4. Why is fluid dynamics important?**

**A4**. Fluid dynamics have importance in our day-to-day life, like in the air conditioning systems & oil pipelines, in the generation of electricity using wind turbines, and in science & technology (rocket engines).

So far, you have studied the theoretical aspects of the mechanical properties of fluids, but this will only take you halfway. For a deeper understanding of these concepts, visuals are essential.

Check out MSVgo**,** an e-learning app developed to facilitate conceptual learning for students of grades 6-12. It is a library of high-quality explanatory videos on the curriculum of CBSE, ICSE, ISC, IGCSE, and IB.