ï»¿ Derive the ascent formula. from Physics Mechanical Properties of Fluids Class 11 Manipur Board

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Derive the ascent formula.

Consider a capillary tube of uniform bore be dipped vertically in a wet liquid. Since liquid is wet, therefore, the meniscus is concave.

Let 'r' be the radius of capillary tube, 'R' be the radius of meniscus and 'θ' the angle of contact.

In figure (i),

X is in atmosphere, Z is at the interface of mercury and atmosphere and Y is on convex side of meniscus.

Therefore, pressure at X and Z is equal and is equal to the atmospheric pressure.

But, pressure at Y is less than that at X and Z by
$\frac{2\mathrm{T}}{\mathrm{R}}$.

Therefore, the liquid is not in equilibrium.

Now, inorder to attain the equilibrium, the liquid will rise in tube.

Let at equilibrium, liquid rise to height h as shown in figure (ii).

Now in the equilibrium condition,

From (1), (2) and (3), we have

,

is the required ascent formula.
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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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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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What is fluid?

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

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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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