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A capillary tube is attached horizontally to a constant pressure head arrangement. If the radius of the capillary tube is increased by 10%, how will the rate of flow of the liquid change?

Answer :

Final answer:

If the radius of the capillary tube is increased by 10%, the flow rate of the liquid shall increase approximately by 46%. This is because the flow rate of a liquid through a capillary tube under constant pressure is proportional to the fourth power of the radius.

Explanation:

The flow rate of a liquid through a capillary tube under constant pressure is proportional to the fourth power of the radius according to Poiseuille's law. If the radius of the capillary tube is increased by 10%, then the flow rate of the liquid shall increase approximately by 46%. This is due to the increased cross-sectional area of the tube, which allows for an increased amount of fluid to flow through.

To understand this, consider the equation given for capillary action 2T cos 0 h = rpg. Here, 'h' is the height the liquid inside the capillary tube relative to the surface of the liquid outside the tube, 'T' is the surface tension of the liquid, '0' is the contact angle between the liquid and the tube, 'r' is the radius of the tube, 'p' is the density of the liquid, and 'g' is gravity. Capillary action can cause liquids to move horizontally (or vertically) over large distances, but the height to which it raises or suppresses a liquid in a tube is limited by the liquid's weight.

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