Examples on Capillary Action
Example 1: A 5 × 10-4 m radius capillary tube is submerged in a mercury-filled beaker. It is discovered that the mercury level inside the tube is 8 × 10-3 m below reservoir level. Identify the angle at which mercury and glass are in contact. Mercury has a surface tension of 0.465 N/m and a density of 13.6 × 103 kg/m3.
Solution:
Given:
- r = 5 × 10-4 m
- h = -8 × 10-3 m
- T = 0.465 N/m
- g = 9.8 m/s2
- ρ = 13.6 × 103 kg/m3
We have,
T = rhρg/2 cos θ
0.465 = (5 × 10-4 × -8 × 10-3 × 13.6 × 103 × 9.8)/(2 cos θ)
cos θ = -40×9.8×13.6×10-4 / 2×0.465
-cos θ = 0.5732
θ = 124o58′
Example 2: If water rises to a height of 12.5 cm inside a capillary tube, and assuming that the angle of contact between the water and the glass is 0°, determine the radius of the tube.
Solution:
Given,
- h = 0.125 m
- T = 72.7 × 10-3 N/m
- θ = 0°, g = 9.8 m/s2
- ρ = 1000 kg/m3
We have,
r = (2Tcos θ)/hρg
r = (2 × 72.7 × 10-3 × cos 0) / (0.125 × 1000 × 9.8)
r = 0. 12 mm
Example 3: Calculate the Height of the capillary tube if the Surface Tension is 32 × 10-3 N/m, the Radius of the capillary tube is 30 m, Density of liquid is 790 kg/m3 at 0° angle of contact.
Solution:
Given,
- r = 30 m
- T = 32 × 10-3 N/m
- θ = 0°
- g = 9.8 m/s2
- ρ = 790 kg/m3
We have,
h = (2Tcos θ)/rρg
h = (2 × 32 × 10-3 × cos 0°) / ( 30 × 790 × 9.8)
h = (64 × 10-3) / (232260)
h = 0.00027 × 10-3 m
Example 4: Calculate the capillary tube’s density if the liquid is at a 45° angle of contact, the surface tension is 2 × 103 N/m, the height is 25 m and the capillary tube’s radius is 21 m.
Solution:
Given,
- r = 21 m
- T = 2 × 103 N/m
- θ = 45°
- h = 25 m
- g = 9.8 m/s2
We have,
h = (2Tcos θ)/rρg
ρ = (2Tcos θ)/rhg
ρ = (2 × 2 × 103 × cos 45°)/(21 × 25 × 9.8)
ρ = 2.8284 × 103 / 5145
ρ = 0.0005 × 103
Capillary Action
Capillary Action in Physics is the action of the liquid in the capillary tubes. Capillary tubes, which are narrow cylindrical tubes, have very small diameters. It is observed that the liquid in the capillary either rises (or) decreases in relation to the level of the surrounding liquid when these tiny tubes are submerged in a liquid. The action of these liquids is called the capillary action and it is an important phenomenon in physics.
Capillary action is caused by the intermolecular attraction of the water molecules and the adhesive force between the capillary walls and the liquid. In this article, we will learn about Capillary Action, the Capillary Action Formula, Its derivation, examples, and others in detail.
Table of Content
- What Is Capillary Action?
- Capillary Action Formula
- Forces in Capillary Action
- Liquid Meniscus in Capillarity
- Difference between Concave, Convex and Plane Meniscus
- Applications of Capillarity
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