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Answer :
Final answer:
The formula for the height of liquid rise in a capillary tube is derived from capillary action and includes the factors of surface tension, fluid density, and tube radius. The formula is given by h = (2T cos(θ)) / (ρ g r). In essence, the height of liquid rise is inversely proportional to the radius of the tube.
Explanation:
Capillary Action and Liquid Rise in Tubes
The formula for the height of liquid rise in a capillary glass tube is derived from the principles of capillary action and is influenced by various factors, including surface tension, density of the liquid, the contact angle, and the radius of the tube. It is mathematically represented as:
h = (2T cos(θ)) / (ρ g r)
Where:
- h: Height of liquid rise in the capillary tube
- T: Surface tension of the liquid
- θ: Contact angle between the liquid and the tube
- r: Radius of the tube
- ρ: Density of the liquid
- g: Acceleration due to gravity (approximately 9.8 m/s²)
For example, in a glass tube (which has a strong attraction to water molecules), the contact angle is typically 0°, resulting in a significant height of water rise due to the strong surface tension of water. Smaller diameter tubes result in greater heights of liquid rise due to the inverse relationship between radius and height as indicated in the formula.
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