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A capillary tube is dipped into water. How high will the water rise in the tube

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Question: A capillary tube is dipped into water. How high will the water rise in the tube if the radius is 1 mm?

Options:

  1. 2.5 cm
  2. 5 cm
  3. 10 cm
  4. 15 cm

Correct Answer: 5 cm

Solution: 

Using the capillary rise formula, h = (2γcosθ)/(ρgr), where γ is surface tension, θ is contact angle, ρ is density, g is acceleration due to gravity, and r is radius.

A capillary tube is dipped into water. How high will the water rise in the tube

Practice Questions

Q1
A capillary tube is dipped into water. How high will the water rise in the tube if the radius is 1 mm?
  1. 2.5 cm
  2. 5 cm
  3. 10 cm
  4. 15 cm

Questions & Step-by-Step Solutions

A capillary tube is dipped into water. How high will the water rise in the tube if the radius is 1 mm?
Correct Answer: Height of water rise will depend on the values of surface tension, contact angle, density, and gravity.
  • Step 1: Identify the formula for capillary rise, which is h = (2γcosθ)/(ρgr).
  • Step 2: Determine the values needed for the formula: surface tension (γ), contact angle (θ), density of water (ρ), acceleration due to gravity (g), and radius (r).
  • Step 3: For water, typical values are: γ = 0.0728 N/m, θ = 0° (cosθ = 1), ρ = 1000 kg/m³, g = 9.81 m/s², and r = 1 mm = 0.001 m.
  • Step 4: Plug the values into the formula: h = (2 * 0.0728 * 1) / (1000 * 9.81 * 0.001).
  • Step 5: Calculate the value of h to find out how high the water will rise in the tube.
  • Capillary Action – The ability of a liquid to flow in narrow spaces without the assistance of external forces, influenced by surface tension and adhesive forces.
  • Surface Tension – The cohesive force at the surface of a liquid that causes it to behave as an elastic sheet.
  • Contact Angle – The angle formed between the tangent to the liquid surface and the solid surface at the contact line.
  • Fluid Density – The mass per unit volume of a fluid, which affects the height to which a liquid can rise in a capillary tube.
  • Gravity – The force that attracts a body toward the center of the earth, affecting the weight of the liquid column in the tube.
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