What is the approximate capillary height of water at 20°C inside a clean glass tube with a 1 mm bore____________________?
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Answer: E. 30 mm
Explanation
Capillary action causes water to rise inside small-diameter glass tubes due to the adhesive forces between water and glass. Surface tension forces pull the liquid column upward until the weight of the water column balances the upward force. For a clean glass tube with a one millimeter bore at room temperature, this hydrostatic balance calculates to roughly thirty millimeters. The height of capillary rise is directly proportional to surface tension and the contact angle, and inversely proportional to tube radius. Water has a high surface tension and wets glass completely, resulting in a contact angle close to zero degrees. Calculating the rise involves multiplying surface tension by two, dividing by the product of density, gravity, and tube radius.
Option A of one millimeter is far too small and underestimates the strong capillary pull exerted by a narrow bore. Options B and C of five or ten millimeters underestimate the theoretical calculation for water in a one-millimeter clean glass tube. Option D of twenty millimeters is closer but still falls short of the thirty millimeter height established by standard fluid calculations.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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