Notes : Define Pressure in Fluid - Formula, Units And Dimensions - Physicskund

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Learn Pressure in Fluids Class 11 Physics with complete NCERT notes. Understand pressure, average pressure, pressure at a point, SI unit, dimensional formula, atmospheric pressure, formulas, FAQs, MCQs, true/false, fill in the blanks, and important questions for CBSE, NEET & JEE - physicskund

Pressure

Pressure is an important physical quantity that describes how a force acts on a surface. Everyday experience shows that both the magnitude of force and the area over which it acts are important. A larger force produces a greater effect, while for the same force, a smaller contact area produces a greater effect. Therefore, pressure depends on both force and area.

Need for Pressure

The effect of a force depends not only on its magnitude but also on the area over which it acts.

Examples

  • A sharp knife cuts easily because its edge has a very small contact area, producing a large pressure.
  • A person can lie safely on a bed of nails because the body weight is distributed over many nails, increasing the contact area and reducing the pressure on each nail.
  • Snow shoes have a large surface area, reducing pressure on snow and preventing a person from sinking.

Pressure Exerted by a Fluid at Rest

When an object is immersed in a fluid at rest, the fluid exerts a force on every point of the object's surface as well as on the walls of the container.

Average Pressure

If a normal force F acts uniformly on a surface of area A, then the average pressure is defined as the normal force acting per unit area.

$$ P_{\mathrm{av}}=\frac{F}{A} \qquad ...(1) $$

where,

Pav = Average pressure

F = Normal force

A = Area of contact

Definition

Average pressure is the normal force acting per unit area.

Pressure at a Point

The average pressure gives the pressure over a finite area. To determine the pressure at an exact point inside a fluid, the area is made extremely small. Pressure at a point is defined as the limiting value of the normal force per unit area as the area approaches zero.

$$ P=\lim_{\Delta A\rightarrow0}\frac{\Delta F}{\Delta A} \qquad ...(2) $$

where,

P = Pressure at a point

\(\Delta F\) = Normal force acting on a very small area

\(\Delta A\) = Very small area on which the force acts

Nature of Pressure

Pressure is a scalar quantity.

Although force is a vector quantity, only its normal component appears in Eqs. (1) and (2). Therefore, pressure has magnitude only and no direction.

Dimensional Formula of Pressure

The dimensional formula of pressure is

$$ [ML^{-1}T^{-2}] $$

SI Unit of Pressure

The SI unit of pressure is Pascal (Pa).

$$ 1~\mathrm{Pa}=1~\mathrm{N\,m^{-2}} \qquad ...(3) $$

One Pascal is the pressure produced when a normal force of 1 N acts uniformly on an area of 1 m².

Blaise Pascal

The SI unit of pressure is named after the French scientist Blaise Pascal (1623–1662) in recognition of his pioneering contributions to the study of fluid pressure.

Atmospheric Pressure

A commonly used unit of pressure is the atmosphere (atm). It is the pressure exerted by the Earth's atmosphere at sea level.

$$ 1~\mathrm{atm}=1.013\times10^{5}~\mathrm{Pa} \qquad ...(4) $$

Important Property

The force exerted by a fluid at rest is always normal (perpendicular) to the surface in contact with the fluid.

Why Does a Fluid Exert Only Normal Force?

Suppose the fluid exerted a tangential (parallel) force on the surface.

  • According to Newton's Third Law, the object would exert an equal and opposite tangential force on the fluid.
  • This tangential force would make the fluid flow along the surface.
  • Since the fluid is at rest, such motion is impossible.

Hence, a fluid at rest exerts only a normal (perpendicular) force on the surface.

Pressure Measuring Device

The normal force exerted by a fluid can be measured using an idealised pressure measuring device.

Construction

The device consists of:

  • An evacuated (vacuum) chamber.
  • A spring.
  • A movable piston of area A.

Working

  • The piston is placed inside the fluid.
  • The surrounding fluid exerts a normal force on the piston.
  • The piston compresses the spring.
  • At equilibrium, the restoring force of the spring becomes equal to the force exerted by the fluid.
  • The spring reading gives the magnitude of the normal force exerted by the fluid.

Figure Explanation

The vacuum chamber ensures that no pressure acts on the inner side of the piston. Therefore, only the pressure of the surrounding fluid acts on the piston, allowing accurate measurement of fluid pressure.

Important Formulae

Average Pressure

$$ P_{\mathrm{av}}=\frac{F}{A} $$

Pressure at a Point

$$ P=\lim_{\Delta A\rightarrow0}\frac{\Delta F}{\Delta A} $$

SI Unit of Pressure

$$ 1~\mathrm{Pa}=1~\mathrm{N\,m^{-2}} $$

Atmospheric Pressure

$$ 1~\mathrm{atm}=1.013\times10^{5}~\mathrm{Pa} $$

Key Points

  • Pressure is the normal force acting per unit area.
  • Pressure depends on both the magnitude of force and the area of contact.
  • For the same force, a smaller contact area produces greater pressure.
  • A fluid at rest exerts force only perpendicular (normal) to the surface.
  • Pressure at a point is obtained by taking the limiting value as the area approaches zero.
  • Pressure is a scalar quantity.
  • The SI unit of pressure is Pascal (Pa).
  • The dimensional formula of pressure is $[ML^{-1}T^{-2}]$.
  • $1~\mathrm{atm}=1.013\times10^{5}~\mathrm{Pa}$.

Frequently Asked Questions (FAQs)

1. What is pressure?

Pressure is the normal force acting per unit area.

2. Why is pressure a scalar quantity?

Pressure is a scalar quantity because only the normal component of force is considered.

3. What is the SI unit of pressure?

The SI unit of pressure is Pascal (Pa).

4. Why does a fluid at rest exert only normal force?

A tangential force would make the fluid flow. Since the fluid is at rest, it exerts only a normal force.

5. What is atmospheric pressure?

Atmospheric pressure is the pressure exerted by the Earth's atmosphere at sea level.

6. What is one Pascal?

One Pascal is the pressure produced when a normal force of 1 N acts on an area of 1 m².

Multiple Choice Questions (MCQs)

1. Pressure is defined as

A. Force × Area
B. Normal Force/Area
C. Area/Force
D. Mass/Volume

Answer: B. Normal Force/Area

2. The SI unit of pressure is

A. Newton
B. Joule
C. Pascal
D. Watt

Answer: C. Pascal

3. Pressure is a

A. Vector quantity
B. Scalar quantity
C. Tensor quantity
D. None of these

Answer: B. Scalar quantity

4. A fluid at rest exerts force

A. Parallel to the surface
B. Perpendicular to the surface
C. At 45° to the surface
D. Along the direction of motion

Answer: B. Perpendicular to the surface

5. One atmosphere is equal to

A. 1013 Pa
B. 1.013 × 105 Pa
C. 105 N
D. 1 N m-2

Answer: B. 1.013 × 105 Pa

True or False

1. Pressure is a scalar quantity. True

2. A fluid at rest exerts tangential force. False

3. The SI unit of pressure is Pascal. True

4. Pressure depends on force and area. True

5. 1 atm= $1.013\times10^{5}Pa$ True

Fill in the Blanks

1. Pressure is the __________ force acting per unit area.

Answer: Normal

2. The SI unit of pressure is __________.

Answer: Pascal

3. Pressure is a __________ quantity.

Answer: Scalar

4.A fluid at rest exerts force __________ to the surface.

Answer: Perpendicular (Normal)

5. 1atm =________Pa

Answer: $1.013\times10^{5}$

Very Short Answer Questions

1. Define pressure.

Pressure is the normal force acting per unit area.

2. Write the SI unit of pressure.

Pascal (Pa).

3. Write the dimensional formula of pressure.

$[ML^{-1}T^{-2}]$

4. Is pressure a scalar or vector quantity?

Pressure is a scalar quantity.

5. Write the value of one atmosphere.

$1~\mathrm{atm}=1.013\times10^{5}~\mathrm{Pa}$

Short Answer Questions

1. Define average pressure.

Average pressure is the normal force acting per unit area.

$ P_{\mathrm{av}}=\frac{F}{A} $

2. Why is pressure a scalar quantity?

Pressure is a scalar quantity because it depends only on the normal component of force.

3. Why does a fluid at rest exert only normal force?

If a tangential force acted on the fluid, it would make the fluid flow. Therefore, a fluid at rest exerts only normal force.

4. State the SI unit and dimensional formula of pressure.

SI Unit: Pascal (Pa)

$$ [ML^{-1}T^{-2}] $$

5. What is atmospheric pressure?

Atmospheric pressure is the pressure exerted by the Earth's atmosphere at sea level.

$$ 1~\mathrm{atm}=1.013\times10^{5}~\mathrm{Pa} $$

Long Answer Questions

1. Define pressure and derive the expression for average pressure.

Pressure is defined as the normal force acting per unit area. If a normal force F acts uniformly on an area A, then the average pressure is

$$ P_{\mathrm{av}}=\frac{F}{A} $$

2. Explain why a fluid at rest exerts force only perpendicular to the surface.

If a tangential force existed, it would make the fluid flow. Since a fluid at rest cannot flow, it exerts only a normal (perpendicular) force on the surface.

3. Explain pressure at a point.

Pressure at a point is the limiting value of the normal force acting per unit area as the area approaches zero.

$$ P=\lim_{\Delta A\rightarrow0}\frac{\Delta F}{\Delta A} $$

4. Discuss the SI unit, dimensional formula and nature of pressure.

The SI unit of pressure is Pascal (Pa).

$$ 1~\mathrm{Pa}=1~\mathrm{N\,m^{-2}} $$

The dimensional formula is

$$ [ML^{-1}T^{-2}] $$

Pressure is a scalar quantity because it depends only on the normal component of force.

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