Mechanical Properties of Fluids
Class 11 Physics · Physics Part II · Chapter 2
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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.
Extra questions & answers
Try one from this chapter
Pressure at a depth h in a liquid of density \(\rho\) is given by: