derive the expression for ascent formula

Consider a glass capillary with uniform and fine bore of radius r, which is open at both the ends and dipped vertically in a liquid that wets glass. As soon as the capillary tube is dipped in water, the water creeps up along the glass wall due to force of adhesion between water and glass molecules. The adhesion of liquid to the walls of a capillary causes an upward force on the liquid at the edges and results in a meniscus, which turns upward. The surface tension acts to hold the surface intact, so instead of just the edges moving upward, the whole liquid surface is dragged upward. The vertical force due to surface tension pulls the liquid upwards.
Let q be the angle of contact, r be the density and T be the surface tension of the liquid.
The liquid surface is in contact with the walls of the tube all along a horizontal circle called as circle of contact. If r is the radius of the capillary tube, then the circumference of the circle of contact is 2pr.
Since the liquid surface has a tendency to contract, it pulls the tube inward all along the circumference of the circle with a force T acting per unit length. According to Newton's third law of motion, the tube will give an equal and opposite reaction force to the meniscus of the liquid. The reaction N (which equals T) at each point along the circle of contact can be resolved into two rectangular components:

1. Horizontal component N sinq acting radially outwards. The horizontal component at any point along the circle of contact is cancelled by an equal and opposite component at other end of the diameter. These components cancel out each other. Moreover, horizontal components cannot be responsible for the vertical rise of the liquid
2. Vertical component N cosq acting vertically upwards.

Since all the vertical components N cosq act in the same direction along the circle of contact, the total upward force on the liquid, F = 2pr� N cosq = 2pr� T cosq (^..^. N = T) �(1)

As the liquid rises, its weight increases and at a particular height say 'h', the force due to surface tension in the upward direction becomes equal to the weight of the liquid in the downward direction. The liquid then ceases to rise.
The weight of the liquid in the capillary, W = (Volume of cylindrical liquid column of height h + Volume of the liquid in meniscus) � r � g,
where g is the acceleration due to gravity.
Now, volume of cylindrical liquid column = pr²h
For convenience, we consider the meniscus as to be hemispherical in shape.
Volume of the liquid in the meniscus = Volume of cylinder of height h and radius r - Volume of hemisphere = pr²� r - 1 4 pr³ = pr³ - 2 pr³ 2 3 3 = 1 pr³ 3 Weight of the liquid in the capillary W= pr²h + 1 pr³





W = pr² h + r � r � g�(2) 3 In the equilibrium position, F = W
Equating equations (1) and (2), we get 2pr� T cosq = pr² h + r � r � g 3 T = r h + r � r � g 3 �(3) 2cosq When the tube is of very fine bore, r h. 3
Neglecting r as compared to h in equation (3), we get, 3 T = hrgr 2cosq h = 2Tcosq rrg
This expression is called the ascent formula.

In Perdeep's fundamental physics

Please find this answer

Explain torsion of cylinder

Follow this link https://youtu.be/nxqxXSG1LZM

Best answer

This answer is best

h=2Tcos○/r×rho×g

👍👍

Consider a capillary tube of radius r dipped in a liquid of a surface tension and density suppose the liquid wets sides of tube . Then it's meniscus will be concave . The shape of meniscus of water will be nearly spherical if the cappilary tube is of sufficient narrow bore.

Dear student 1st u have to sign in then in the information page it will ask u which class do u want.. Ok all the best??

Please find this answer

Please find this answer

Exaplain aristotle fallacy?

Please find this answer

Hope this helps you..!!

Its given in study material

jo dislike kra wo gya 
chup chap like thoko
 

Kush pata hai

Why it is dangerous to stand behind a running engine of a vehicle