Question

Obtain an expression for the rise and fall of liquid in a capillary tube using pressure difference.
CHP- MECHANICAL PROPERTY OF FLUID​

Answer 1

Introducing VIP - Your Progress Is Our Responsibility

KNOW MORE

filledbookmark

USE APP

Sign in

Questions & Answers

CBSE

Physics

Grade 11

Capillarity

Question

Answers

Related Questions

Obtain an expression for the rise of a liquid in a capillary tube.

Answer

VerifiedVerified

62.1K+ Views

Hint: A liquid can climb up the capillary tube due to the surface tension. The factors that determine the height of the fluid raised inside a capillary tube are the surface tension of the liquid, the radius of the capillary tube, the curvature of the meniscus, density of the liquid, and the acceleration due to gravity.

Complete step by step solution

Consider a capillary tube or radius r that is open at both ends. When this capillary tube is kept vertical and dipped into a liquid of density ρ , the wetting liquid rises in the tube because of the surface tension, σ .

The lower end of the tube is in contact with water while its upper end is in contact with air, therefore liquid only rises to a definite height h , so that the atmospheric pressure balances out the upward force caused by the surface tension of the liquid.

When the liquid rises, it forms an upward concave shaped meniscus. And thus the angle made by the vertical and tangent through the meniscus is θ<90∘ .

The weight of the liquid that rises in the tube is given by,

W=mg

where m is the mass of the liquid and g is the acceleration due to gravity.

We know that the density is given by,

ρ=mv

⇒m=ρv

And the volume of the liquid that rises can be given by,

v=πr2h

By substituting all these values in the formula of weight,

We obtain the weight of the liquid that rises as,

W=mg=ρπr2hg

Now, the surface tension acts tangentially to the surface of the concave meniscus that is formed, therefore the tensile force in the vertical direction is given by,

Ty=σcosθ×2πr

⇒Ty=2σπrcosθ

When the liquid rises up to its full height, the vertical component of the surface tension and the weight of the liquid balance each other.

Therefore, equating both of these values, we have-

Ty=W

⇒2σπrcosθ=ρπr2hg

⇒h=2σcosθρrg

Therefore the expression for the rise of liquid is obtained.

Note

A liquid only rises in a capillary tube if it is a wetting liquid. The adhesive forces dominate the cohesive forces in a wetting liquid. The liquid particles tend to be attracted more to the surface of the container as compared to their own molecules, thus the liquid climbs up the capillary tube.

Answer 2

Answer:

• When a liquid is inserted into a glass capillary tube, the liquid rises in the capillary against gravity. Therefore, at the point of contact, the weight of the liquid column must be equal to and in opposition to the component of force caused by surface tension.

• The circle of the capillary is equal to the length of the liquid in contact there.

Let   h=height of liquid level in the tube

and r=radius of the capillary tube

       T is the liquid's surface tension,

       R is its density,

and g is the acceleration brought on by gravity.

• The force of magnitude $f_{T}$ is given as $f_{T}$= $T*$$2\pi r$ and acts tangentially on a unit length of liquid surface that is in contact with the capillary tube wall.

There are two parts to this force that can be separated:

a. $f_{T}$cosФ- vertically upward and

b. $f_{T}$sinФ- along horizontal

• The vertical element works well. The capillary increase is not caused by the horizontal component.

$(f_{T})_{V}$ = force per unit length * circumference

         = TcosФ * $2\pi r$

we get,

              $W = mg = Vrg=$ $\pi r^{2}hpg$

Where, V is the volume of the liquid rise in the tube (ignoring the liquid in the concave meniscus)

and m is the mass of the liquid in the capillary rise,

• This has to be equal to and in the opposite direction as the vertical  component of the surface tension force.

• If the meniscus's liquid is ignored, the force caused by surface tension must be considered for balance.

               ∴$2\pi r T cos$Ф$= \pi r^{2}hpg$

                   ∴$h=\frac{2Tcos}{rpg}$   .....(1)

∴ This is the required expression for the rising or fall od liquid in a capillary tube.