Maharashtra Board Class 12 Physics Chapter 2 Mechanical Properties of Fluids PDF Download

2. Mechanical Properties of Fluids

2.1 Introduction:

In XIth Standard, we discussed how solids behave under the action of a force. Among three states of matter - solid, liquid and gas - a solid nearly keeps its fixed shape and volume even if a large force is applied to it. Liquids and gases do not have their own shape. They take the shape of the container they are kept in. Due to this, liquids and gases flow when an outside force is applied to them. A fluid means a substance that can flow. Therefore, liquids and gases together are called fluids. A fluid either has no rigidity or its rigidity is very low.

In our daily life, we often feel the pressure exerted by a fluid at rest and in motion. Viscosity and surface tension play an important role in nature. We will try to understand such properties in this chapter.

2.2 Fluid:

Any substance that can flow is a fluid. A fluid is a substance that deforms continuously under the action of an outside force. Fluid is a phase of matter that includes liquids, gases and plasmas.

A fluid flows under the action of a force or a pressure gradient. Behaviour of a fluid in motion is normally complicated. We can understand fluids by making some simple assumptions. We introduce the concept of an ideal fluid to understand its behaviour. An ideal fluid has the following properties:

1. It is incompressible: its density is constant.

2. Its flow is irrotational: its flow is smooth, there are no turbulences in the flow.

3. It is nonviscous: there is no internal friction in the flow, that is, the fluid has no viscosity. (viscosity is discussed in section 2.6.1)

4. Its flow is steady: its velocity at each point is constant in time.

It is important to understand the difference between a solid and a fluid. Solids can be subjected to shear stress (tangential stress) as shown in Fig. 2.1 and normal stress, as shown in Fig. 2.2.

Solids oppose the shear stress either by developing a restoring force, which means that the deformations are reversible, or they require a certain initial stress before they deform and start flowing. (We have studied this behaviour of solids in XIth Standard.)

Ideal fluids, on the other hand, can only be subjected to normal, compressive stress (called pressure). Most fluids offer a very weak resistance to deformation. Real fluids display viscosity and so are capable of being subjected to low levels of shear stress.

We shall discuss mechanical properties of only liquids and gases in this chapter. The shear modulus of a fluid is zero. In simpler words, fluids are substances which cannot resist any shear force applied to them. Air, water, flour dough, toothpaste, etc., are some common examples of fluids. Molten lava is also a fluid.

Teacher's Note

Fluids are everywhere around us. When you drink water or ride a bicycle, you are using fluids. Water flows from taps, and air pushes things. Understanding fluids helps us know how things move and work in our daily life.

Exam Trick

Remember: Fluids have no fixed shape. Just like water takes the shape of a cup, all fluids change their shape. Solids do not do this - they keep their shape.

Points to Remember

A fluid is any substance that can flow and change shape.

Liquids and gases are both fluids.

Fluids cannot resist shear force like solids can.

An ideal fluid has no viscosity and no friction inside.

Real fluids like water and oil have some viscosity.

2.2.1 Fluids at Rest:

The branch of physics which deals with the properties of fluids at rest is called hydrostatics. In the next few sections we will consider some of the properties of fluids at rest.

2.3 Pressure:

A fluid at rest exerts a force on the surface of contact. The surface may be a wall or the bottom of an open container of the fluid. The normal force (F) exerted by a fluid at rest per unit surface area (A) of contact is called the pressure (p) of the fluid.

\[p = \frac{F}{A}\]

Thus, an object having small weight can exert high pressure if its weight acts on a small surface area. For example, a force of 10 N acting on 1 cm² results in a pressure of 10⁵ N m⁻². On the other hand, the same force of 10 N while acting on an area of 1 m², exerts a pressure of only 10 N m⁻².

The SI unit of pressure is N/m². Also, 1 N/m² = 1 Pascal (Pa). The dimension of pressure is [L⁻¹M¹T⁻²]. Pressure is a scalar quantity. Other common units of measuring pressure of a gas are bar and torr.

1 bar = 10⁵ Nm⁻²

1 hectapascal (hPa) = 100 Pa

Note: 1 N weight is about 100 g mass, if g = 10 m s⁻².

Teacher's Note

Pressure is how hard something pushes on a surface. When you stand on the ground, your weight creates pressure. A small pin pushes harder on your skin than your whole hand because it has a smaller area.

Exam Trick

Remember: Pressure = Force ÷ Area. If you press with the same force on a smaller area, the pressure becomes more. This is why a needle can hurt your skin but your whole hand cannot.

Points to Remember

Pressure is the force acting per unit area.

The SI unit of pressure is Newton per square meter (N/m²) or Pascal (Pa).

Smaller area means more pressure for the same force.

Pressure is a scalar quantity.

Atmospheric pressure at sea level is about 101325 Pa.

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