Question
Derive the ascent formula.
Solution
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 .
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.
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 .
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.
