Mechanical Properties of Fluids

Physics Part II

Physics

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What is the pressure inside a drop of mercury of radius 3.00 mm at room temperature? Surface tension of mercury at that temperature (20°C) is 0.465N/m. The atmospheric pressure is 1.01 x10^{5} Pa. Also give the excess pressure inside the drop.

Given,

Radius of drop of mercury, r = 3.0 mm

Surface tension of mercury = 0.465 N/m

Atmospheric pressure, P

Excess of pressure inside the liquid drop is given by,

$\mathrm{p}=\frac{2\mathrm{T}}{\mathrm{R}}\phantom{\rule{0ex}{0ex}}\mathrm{Here},\phantom{\rule{0ex}{0ex}}T=0.465\mathrm{N}/\mathrm{m}\phantom{\rule{0ex}{0ex}}\mathrm{R}=3\mathrm{mm}=3\times {10}^{-3}\mathrm{m}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore Excesspressure,\mathrm{p}=\frac{2\times 4.65\times {10}^{-1}}{3\times {10}^{-3}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=310\mathrm{Pa}\phantom{\rule{0ex}{0ex}}=0.0031\times {10}^{5}\mathrm{Pa}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Pressure}\mathrm{inside}\mathrm{the}\mathrm{drop}={\mathrm{P}}_{0}+\mathrm{p}\phantom{\rule{0ex}{0ex}}=1.01\mathrm{x}{10}^{5}+0.0031\times {10}^{5}\mathrm{Pa}\phantom{\rule{0ex}{0ex}}=1.0131\times {10}^{5}\mathrm{Pa}$

$\mathrm{p}=\frac{2\mathrm{T}}{\mathrm{R}}\phantom{\rule{0ex}{0ex}}\mathrm{Here},\phantom{\rule{0ex}{0ex}}T=0.465\mathrm{N}/\mathrm{m}\phantom{\rule{0ex}{0ex}}\mathrm{R}=3\mathrm{mm}=3\times {10}^{-3}\mathrm{m}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore Excesspressure,\mathrm{p}=\frac{2\times 4.65\times {10}^{-1}}{3\times {10}^{-3}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=310\mathrm{Pa}\phantom{\rule{0ex}{0ex}}=0.0031\times {10}^{5}\mathrm{Pa}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Pressure}\mathrm{inside}\mathrm{the}\mathrm{drop}={\mathrm{P}}_{0}+\mathrm{p}\phantom{\rule{0ex}{0ex}}=1.01\mathrm{x}{10}^{5}+0.0031\times {10}^{5}\mathrm{Pa}\phantom{\rule{0ex}{0ex}}=1.0131\times {10}^{5}\mathrm{Pa}$

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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.

799 Views

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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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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