Calculating Capillary Height with Surface Tension: A Question on Homework

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SUMMARY

The discussion focuses on calculating the height of water in a capillary tube, balancing the upward force due to surface tension with the weight of the liquid. The upward force is determined using the formula \( (2\pi r) T \), where \( T \) is the surface tension of water, measured at \( 6 \times 10^{-2} \, \text{Nm}^{-1} \). The force due to the weight of the liquid is given as \( 7.5 \times 10^{-4} \, \text{N} \). Participants confirm that the approach of equating the upward force to the weight of the liquid is correct.

PREREQUISITES
  • Understanding of capillary action and surface tension
  • Familiarity with the formula for excess pressure in a liquid column
  • Basic knowledge of fluid mechanics
  • Ability to manipulate algebraic equations
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  • Study the derivation of the capillary rise formula in detail
  • Explore the effects of different liquids on capillary height
  • Learn about the role of contact angle in capillary action
  • Investigate applications of capillary action in various scientific fields
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Students studying fluid mechanics, physics educators, and anyone interested in the practical applications of surface tension and capillary action in liquids.

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Homework Statement


[/B]
Water rises in a capillary tube to certain height such that the upward surface due to surface tension is balanced by 7.5 X 10-4N
Force due to weight of the liquid. If the surface tension of water is 6 X 10-2Nm-1,the inner circumference of the capillary must be

Homework Equations



pexcess=2T/rcosθ

The Attempt at a Solution



I thought that the force of the excess pressure which causes the movement of liquid must be equal to the weight of the liquid.I know excess pressure is 2T/r (θ=0 for water),but how to find the force of this pressure?Is my approach right?

Can we just like that multiply 2T/r with πr2because it is not plain liquid but a meniscus?
 
Physics news on Phys.org
Yes. The upward force is ##(2\pi r) T##. Think of the surface as a membrane with a tensile force per unit length of T.
 

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