Mechanical Properties of Fluids

Physics Part II

Physics

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A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. If 15.0 cm of water and spirit are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6).

The mercury column in two arms are in level with 10cm of water in one arm and 12.5cm of spirit in the second arm.

Thus the density of spirit is,${\mathrm{\rho}}_{\mathrm{s}}=\frac{10}{12.5}\times 1=0.8\mathrm{gm}/\mathrm{cc}$

Let the difference in the level of mercury in two arms be x, on adding 15.0cm of water and 15.0cm of spirit in respective limbs.

Now,

Pressure due to 25 cm of water = Pressure due to x cm of mercury + Pressure due to 27.5 cm of spirit

${\mathrm{\rho}}_{\mathrm{w}}{\mathrm{h}}_{\mathrm{w}}\mathrm{g}={\mathrm{\rho}}_{\mathrm{hg}}\mathrm{xg}+{\mathrm{\rho}}_{\mathrm{s}}{\mathrm{h}}_{\mathrm{s}}\mathrm{g}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{\rho}}_{\mathrm{w}}{\mathrm{h}}_{\mathrm{w}}={\mathrm{\rho}}_{\mathrm{hg}}\mathrm{x}+{\mathrm{\rho}}_{\mathrm{s}}{\mathrm{h}}_{\mathrm{s}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow 25\times 1=(13.6)\mathcal{x}+(0.8)(27.5)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \mathcal{x}=\frac{25-(0.8)(27.5)}{13.6}=0.221cm$
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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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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 fluid?

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

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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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