Chapter 9: Mechanical Properties of Fluids Short Questions | physics Class 11 CBSE

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Chapter 9: Mechanical Properties of Fluids Short Questions | physics Class 11 CBSE | ByteNotes.in

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Question 1

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Define pressure and state its SI unit. Why is pressure a scalar quantity?

Pressure is the normal force exerted per unit area: Pav = F/A; in limiting form P = lim(ΔA→0) ΔF/ΔA.
Its SI unit is pascal (Pa), equivalent to N m⁻², named after French scientist Blaise Pascal.
Pressure is scalar because only the component of force normal to the area appears in its definition — no direction can be assigned to pressure itself.

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Question 2

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State Pascal's Law and give one application in daily life.

Pascal's Law states that pressure in a fluid at rest is the same at all points at the same height, and any external pressure applied to an enclosed fluid is transmitted undiminished and equally in all directions.
This is demonstrated using a horizontal cylinder with multiple vertical tubes — pushing the piston raises the fluid level equally in all tubes.
A practical application is the hydraulic lift, which uses this principle to multiply a small applied force into a large lifting force capable of raising cars.

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Question 3

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Derive the expression for pressure at a depth h in a liquid of density ρ open to atmosphere.

Consider a cylindrical fluid element of cross-sectional area A and height h; forces acting vertically are fluid pressure at top (P₁A downward), at bottom (P₂A upward), and weight mg of fluid.
For equilibrium: (P₂ − P₁)A = mg = ρhAg, giving P₂ − P₁ = ρgh.
Setting P₁ = Pa (atmospheric pressure at the surface), the pressure at depth h is P = Pa + ρgh.

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Question 4

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What is gauge pressure? How does a manometer measure it?

Gauge pressure is the excess of actual pressure over atmospheric pressure at a given point: Pg = P − Pa = ρgh.
An open-tube manometer consists of a U-tube with one end connected to the system and the other open to atmosphere.
The gauge pressure of the system is proportional to the height difference h of the liquid columns in the two arms of the manometer.

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Question 5

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Explain the hydrostatic paradox with an example.

Hydrostatic paradox refers to the fact that liquid pressure depends only on the vertical height of the fluid column, not on the shape or cross-sectional area of the container.
Consider three vessels A, B, and C of different shapes connected at the bottom by a horizontal pipe — when filled with water, the level is identical in all three vessels.
This occurs because water at the bottom experiences the same pressure Pa + ρgh below each section regardless of vessel shape, so it rises to the same height in each.

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Question 6

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Describe the working principle of a mercury barometer.

A long glass tube closed at one end is filled with mercury and inverted into a trough of mercury; the space above the mercury column contains only mercury vapour whose pressure is negligible.
The atmospheric pressure Pa supports the mercury column of height h, so Pa = ρgh where ρ is the density of mercury.
At sea level the mercury column is about 76 cm high, equivalent to 1 atm (1.013 × 10⁵ Pa); a drop of 10 mm or more signals an approaching storm.

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Question 7

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Define steady flow (streamline flow) and state the condition for two streamlines not to intersect.

Flow is said to be steady if at any given fixed point in space the velocity of each passing fluid particle remains constant in time, though velocity may differ from point to point.
A streamline is a curve whose tangent at any point gives the direction of fluid velocity at that point.
Two streamlines cannot cross because at the point of intersection a fluid particle would have two possible velocities, making the flow unsteady — contradicting the definition of steady flow.

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Question 8

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State and explain the equation of continuity for incompressible fluid flow.

For incompressible fluid flow in a pipe, the equation of continuity states Av = constant, where A is the cross-sectional area and v is the fluid speed at that cross-section.
This equation is a statement of conservation of mass: the mass of fluid crossing any cross-section per unit time must be the same throughout a pipe with no leaks.
Consequently, where the pipe is narrower (smaller A) the fluid moves faster (larger v), and where the pipe is wider the fluid slows down.

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Question 9

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State Bernoulli's equation and identify the physical meaning of each term.

Bernoulli's equation states: P + ½ρv² + ρgh = constant along a streamline for ideal (non-viscous, incompressible) steady fluid flow.
The term P represents the pressure energy per unit volume of the fluid at that point.
The term ½ρv² is the kinetic energy per unit volume and ρgh is the gravitational potential energy per unit volume; their sum remains constant as one moves along a streamline.

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Question 10

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State Torricelli's Law and derive the speed of efflux for a tank open to atmosphere.

Torricelli's Law states that the speed of efflux of fluid from a small hole in an open tank at depth h below the free surface is v₁ = √(2gh).
Applying Bernoulli's equation at the free surface (point 2) and the hole (point 1), with P at both points equal to Pa and v₂ ≈ 0 (large tank), gives Pa + ρgy₂ = Pa + ½ρv₁² + ρgy₁.
Simplifying with y₂ − y₁ = h gives v₁ = √(2gh), identical to the speed of a freely falling body from height h.

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Question 11

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What is dynamic lift? Explain the Magnus effect.

Dynamic lift is the force that acts on a body such as an aircraft wing or spinning ball by virtue of its motion through a fluid, arising from pressure differences due to velocity differences.
When a ball spins, it drags air along with it; the velocity of air is higher above the ball and lower below it (or vice versa depending on direction of spin), creating a pressure difference.
This net pressure difference produces an upward (or sideward) force called the Magnus effect, causing the ball to deviate from its parabolic trajectory in games like cricket and tennis.

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Question 12

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Define coefficient of viscosity. Write its SI unit and dimensions.

The coefficient of viscosity η of a fluid is defined as the ratio of shearing stress to the strain rate: η = (F/A)/(v/l) = Fl/(vA).
Its SI unit is poiseuille (Pl), which is equivalent to N s m⁻² or Pa·s.
The dimensions of viscosity are [ML⁻¹T⁻¹]; thin liquids like water have lower η while thick liquids like glycerine have higher η.

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Question 13

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How does temperature affect the viscosity of liquids and gases? Give reason.

The viscosity of liquids decreases with increasing temperature because higher temperature gives molecules more kinetic energy, reducing intermolecular cohesive forces that cause internal friction.
In gases, viscosity increases with temperature because higher temperature increases random molecular motion, resulting in more frequent momentum transfer between layers.
This opposite behaviour is evident in practical situations — engine oil thins out on heating, while air and other gases become slightly more viscous at higher temperatures.

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Chapter 9: Mechanical Properties of Fluids | Short Questions

Define pressure and state its SI unit. Why is pressure a scalar quantity?

State Pascal's Law and give one application in daily life.

Derive the expression for pressure at a depth h in a liquid of density ρ open to atmosphere.

What is gauge pressure? How does a manometer measure it?

Explain the hydrostatic paradox with an example.

Describe the working principle of a mercury barometer.

Define steady flow (streamline flow) and state the condition for two streamlines not to intersect.

State and explain the equation of continuity for incompressible fluid flow.

State Bernoulli's equation and identify the physical meaning of each term.

State Torricelli's Law and derive the speed of efflux for a tank open to atmosphere.

What is dynamic lift? Explain the Magnus effect.

Define coefficient of viscosity. Write its SI unit and dimensions.

How does temperature affect the viscosity of liquids and gases? Give reason.

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