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Grade upto college level Mechanics

A solid glass rod of radius r = 1.3 cm is placed inside and coaxial with a glass cylinder of internal radius R = 1.7 cm. Their bottom ends are aligned and placed in contact with, and perpendicular to, the surface of an open tank of water (see Fig. 15-30). To what height will the water rise in the region between the rod and the cylinder? Assume that the angle of contact is 0° and use 72.8 mN/m for the surface tension of water.
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

Profile image of Shane Macguire
11 Years agoGrade upto college level
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1 Answer

Profile image of Deepak Patra
11 Years ago

When a solid glass rod is placed inside a glass cylinder, the water will rise to a certain height between the two objects due to surface tension. To calculate this height, we can use the concept of capillary rise.

Calculating Capillary Rise

To determine the height to which the water will rise between the rod and the cylinder, we can use the formula for capillary rise:

\[ h = \dfrac{2T \cdot cos(\theta)}{ρgr} \]
  • h = height of capillary rise
  • T = surface tension of water (72.8 mN/m)
  • θ = angle of contact (0° for glass)
  • ρ = density of water
  • g = acceleration due to gravity
  • r = radius of the glass rod

Substitute Values and Calculate

Substitute the given values into the formula:

\[ h = \dfrac{2 \times 72.8 \times 10^{-3} \times cos(0°)}{1000 \times 9.81 \times 0.013} \]

Solve for Height

After calculating the equation, you will find the height to which the water will rise between the rod and the cylinder. This calculation is crucial for understanding the capillary action between two solid objects immersed in a liquid.

Remember that the height of capillary rise is influenced by the surface tension of the liquid, the angle of contact, and the radius of the objects involved. This phenomenon is an essential aspect of fluid mechanics and plays a significant role in various natural and artificial systems.