A glass tube of inner diameter of 1 mm, outer diameter of 1.1 mm. It is kept vertical and partially dipped in water. Calculate the downward pull due to surface tension. (Surface tension of water = 75 dyne/cm)

To calculate the downward pull due to surface tension on a glass tube partially dipped in water, we need to consider a few key concepts related to surface tension and the geometry of the tube. The surface tension creates a force that acts along the surface of the liquid, and this force can be calculated using the formula:

Understanding Surface Tension Force

Surface tension (γ) is defined as the force per unit length acting along the surface of a liquid. In this case, the surface tension of water is given as 75 dyne/cm. To find the total force due to surface tension acting on the water inside the tube, we can use the following steps:

Step 1: Calculate the circumference of the tube

The circumference (C) of the tube can be calculated using the formula:

C = π × d

Where d is the inner diameter of the tube. Given that the inner diameter is 1 mm, we convert it to centimeters for consistency with the surface tension units:

d = 1 mm = 0.1 cm

Now, substituting the value into the circumference formula:

C = π × 0.1 cm ≈ 0.314 cm

Step 2: Calculate the force due to surface tension

The total force (F) due to surface tension can be calculated by multiplying the surface tension by the circumference:

F = γ × C

Substituting the values we have:

F = 75 dyne/cm × 0.314 cm ≈ 23.55 dyne

Step 3: Direction of the force

This force acts upwards at the surface of the water inside the tube, creating a downward pull on the water column due to the weight of the water. However, since we are interested in the downward pull due to surface tension, we can consider the force calculated as the effective downward pull on the water column.

Final Result

Thus, the downward pull due to surface tension on the water in the glass tube is approximately:

23.55 dyne

This calculation illustrates how surface tension can influence the behavior of liquids in narrow spaces, such as in capillary tubes, and is a fundamental concept in fluid mechanics. If you have any further questions or need clarification on any part of this process, feel free to ask!