Formula of weight of surface water

AI Thread Summary
The weight of water at the surface is described by the formula 2(pi)Rσ(cos angle), where σ represents surface tension and the angle refers to the contact angle of the meniscus. The discussion suggests that this formula relates to a capillary tube inserted into a water reservoir, causing a column of water to rise due to surface tension. The force exerted by surface tension acts along the length of contact, which is determined by the radius of the capillary tube. The participants seek clarification on how the formula components relate to the physical scenario. Understanding these relationships is essential for grasping the principles of fluid mechanics involved in this phenomenon.
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Homework Statement


Why the weight of water at water surface is given by formula 2(pi)Rσ(cos angle) ?

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The Attempt at a Solution

 

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Is there more context to this?
My guess is that a capillary tube has been inserted into water reservoir, resulting in a column of water rising height h (compared with the water remaining in the reservoir). The weight of this column is held up by surface tension in the meniscus. Phi will be the angle of contact of the meniscus.
 
haruspex said:
Is there more context to this?
My guess is that a capillary tube has been inserted into water reservoir, resulting in a column of water rising height h (compared with the water remaining in the reservoir). The weight of this column is held up by surface tension in the meniscus. Phi will be the angle of contact of the meniscus.
how about 2(pi)R ? how it comes?
 
goldfish9776 said:
how about 2(pi)R ? how it comes?
Surface tension is a force per unit length. What is the length of contact between the water surface and the capillary (radius R)?
 

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