Derive an expression for the rise of
liquid in capillary tube and show that the height of the liquid column
supported is directly proportional to the curvature of the tube
Answers
Answer:
Consider a capillary tube of radius r partially immersed into a wetting liquid of density ρ. Let the capillary rise be h and be the angle of contact at the edge of contact of the concave meniscus and glass figure. If R is the radius of curvature of the meniscus then from the figure, r=R cosθ.
Analysing capillary capillary action using Laplace's law for a spherical membrane Surface tension T is the tangential force per unit length acting along the contact line. It is directed into the liquid making an angle with the capillary wall. We ignore the small volume of the liquid in the meniscus. The gauge pressure within the liquid at a depth h, i.e., at the level of the free liquid surface open to the atmosphere, is
p−P
0
=ρ gh ...(1)
By Laplace's law for a spherical membrane, this gauge pressure is
P−P
0
=
R
2T
...(2)
∴ hρ g=
R
2T
=
r
2T cosθ
∴ h=
rρ g
2T cosθ
...(3)
Thus, narrower the capillary tube, the greater is the capillary rise.
From Eq. (3),
=
2T cosθ
hρ rg
...(4)
Equations (3) and (4) are also valid for capillary depression h of a non-wetting liquid. In this case, the meniscus is convex and is obtuse. Then, cosθ is negative but so is h, indicating a fall or depression of the liquid in the capillary. T is positive in both cases.
solution
Answer verified by Toppr
length and has a radius of 1.5×10
−3
m. Blood flows at rate of 10
−7
m
−3
/
