Mechanical Properties of Fluids

Physics Part II

Physics

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A vessel, whose bottom has a hole of diameter 0.2mm, is filled with water. Find the maximum height to which the water can be filled without leaking it from the hole. (Surface tension of water is 70 dyne/cm)

Let the vessel be filled to a height of h.

The force exerted by height column of water will be balanced by surface tension force on the free surface of water at the hole, at equilibrium.

That is,

$\mathrm{\rho gh}\times {\mathrm{\pi r}}^{2}=2\mathrm{\pi r}\times \mathrm{T}\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{h}=\frac{2\mathrm{T}}{\mathrm{rpg}}\phantom{\rule{0ex}{0ex}}\mathrm{He}re,\mathrm{T}=70\mathrm{dyne}/\mathrm{cm}\phantom{\rule{0ex}{0ex}}\mathrm{r}=\mathrm{d}/2=0.1\mathrm{mm}=0.01\mathrm{cm},\phantom{\rule{0ex}{0ex}}\mathrm{\rho}=1\mathrm{gm}/\mathrm{cc},\phantom{\rule{0ex}{0ex}}g=1000\mathrm{cm}/{\mathrm{s}}^{2}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{h}=\frac{2\times 70}{0.01\times 1\times 1000}=14\mathrm{cm}$

So, 'h' is the maximum height to which the water can be filled without leaking it from the hole.

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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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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 hydrodynamics?

Hydrodynamics is the branch of science that studies about the force exerted by the fluids or acting on the fluids.

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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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