Mechanical Properties of Fluids

Physics Part II

Physics

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Show that the force acting on the liquid in equilibrium is perpendicular to the free surface of liquid.

Consider a liquid in a container. The liquid is in an equilibrium condition. Force F is acting on the liquid at angle $\mathrm{\theta}$ with the free surface of liquid as shown in figure below.

On resolving the components of force, we get

Fcos$\mathrm{\theta}$ - component of force along the surface

Fsin$\mathrm{\theta}$ - component of force ormal to the surface

In the equilibrium state, component of force along the surface is 0.

Therefore,

Fcos$\mathrm{\theta}$ = 0

$\Rightarrow \mathrm{cos}\mathrm{\theta}={0}^{\mathrm{o}}\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.,\mathrm{\theta}={90}^{\mathrm{o}}$

On resolving the components of force, we get

Fcos$\mathrm{\theta}$ - component of force along the surface

Fsin$\mathrm{\theta}$ - component of force ormal to the surface

In the equilibrium state, component of force along the surface is 0.

Therefore,

Fcos$\mathrm{\theta}$ = 0

$\Rightarrow \mathrm{cos}\mathrm{\theta}={0}^{\mathrm{o}}\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.,\mathrm{\theta}={90}^{\mathrm{o}}$

So, the force must be normal to surface.

Thus, the free surface of liquid in equilibrium adjusts normal to the direction of force acting on it.

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Do intermolecular or inter-atomic forces follow inverse square law?

No. Intermolecular and inter-atomic forces do not obey the inverse square law.

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What is hydrostatics?

Hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. The study of fluids at rest or objects placed at rest in fluids is hydrostatics.

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Why solids have definite shape while liquids do not have definite shape?

Solids: Intermolecular forces are very strong and thermal agitations are not sufficiently strong to separate the molecules from their mean position. Solids are rigid and hence they have definite shapes.

Liquids: In liquids intermolecular forces are not sufficiently strong to hold the molecules at definite sites, as a result they move freely within the bulk of liquid, therefore, do not possess definite shapes. Liquids take the same shape as that of the container.

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What is fluid?

Any material that can flow is a fluid. Liquids and gases are examples of fluid.

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