What went wrong when the king rode under the arch?

It was too low and knocked off his crown

How does the chain of blame unfold in the poem?

Each accused person blames another, ending with the king's own changes

Why is pressure in a fluid a scalar?

At any point a fluid at rest exerts the same pressure in all directions, so it has no specific direction and is treated as a scalar.

How does pressure vary with depth in a liquid?

It increases linearly with depth, \(P=P_0+\rho gh\), where \(P_0\) is the pressure at the surface.

State Pascal's law and give an application.

Pressure applied to an enclosed fluid is transmitted equally to all points; it is used in the hydraulic lift and hydraulic brakes.

State the equation of continuity.

For an incompressible fluid in steady flow, the product of cross-sectional area and speed is constant, \(A_1v_1=A_2v_2\).

State Bernoulli's principle.

Along a streamline of an ideal fluid, \(P+\tfrac12\rho v^{2}+\rho gh=\) constant, expressing conservation of energy.

Define the coefficient of viscosity.

It is the tangential viscous force per unit area per unit velocity gradient between fluid layers; SI unit \(\text{Pa s}\).

What is terminal velocity?

The constant maximum velocity attained by a body falling through a viscous fluid when the viscous drag (by Stokes' law) balances the net weight.

What does the Reynolds number determine?

Whether flow is laminar (below a critical value, about 1000) or turbulent (above about 2000).

Define surface tension and surface energy.

Surface tension is the force per unit length along a liquid surface; surface energy is the work done per unit increase in surface area, numerically equal to the surface tension.

Why does liquid rise in a capillary tube?

Surface tension and the angle of contact produce a net upward force, giving capillary rise \(h=2S\cos\theta/(\rho g r)\).

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Chapter 2: Mechanical Properties of Fluids — Class 11 Physics

Physics · 14 chapters

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Chapter 2: Mechanical Properties of Fluids

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Pressure at a depth h in a liquid of density \(\rho\) is given by:

Summary

Liquids and gases are fluids because they flow and offer very little resistance to shear stress. Pressure is the normal force per unit area; in a fluid at rest it acts equally in all directions (a scalar) and increases with depth as \(P=P_0+\rho gh\). Pascal's law states that a pressure applied to an enclosed fluid is transmitted undiminished to every point, the basis of the hydraulic lift and brakes. Atmospheric pressure is measured by a barometer. For an ideal fluid in steady streamline flow the equation of continuity, \(Av=\) constant, expresses conservation of mass, and Bernoulli's principle, \(P+\tfrac12\rho v^{2}+\rho gh=\) constant, expresses conservation of energy, explaining the lift on an aerofoil and the working of a venturimeter. Real fluids have viscosity, an internal friction described by the coefficient \(\eta\); Stokes' law gives the viscous drag on a sphere and leads to terminal velocity. Flow is laminar below a critical Reynolds number and turbulent above it. Surface tension arises from intermolecular attraction at a liquid surface, giving rise to excess pressure inside drops and bubbles, capillary rise, and angle of contact, with surface energy equal to surface tension times area.

Pressure and its variation with depthPascal's law and hydraulic machinesStreamline flow and equation of continuityBernoulli's principle and applicationsViscosity, Stokes' law and terminal velocityReynolds numberSurface tension, capillarity and angle of contact

Key terms

Pressure

The normal force exerted by a fluid per unit area, a scalar that increases with depth as \(P=P_0+\rho gh\).

Pascal's law

Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and the container walls.

Equation of continuity

For steady flow of an incompressible fluid, \(Av=\) constant, expressing conservation of mass.

Bernoulli's principle

For an ideal fluid in streamline flow, \(P+\tfrac12\rho v^{2}+\rho gh\) is constant along a streamline.

Viscosity

The internal friction of a fluid that opposes relative motion between its layers, measured by the coefficient \(\eta\).

Surface tension

The property by which the free surface of a liquid behaves like a stretched membrane, equal to surface energy per unit area.

Important questions

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The normal force exerted by a fluid per unit area, a scalar that increases with depth as \(P=P_0+\rho gh\).

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Practice quiz · Mechanical Properties of Fluids

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Mechanical Properties of Fluids

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