Maximum Capillary Rise: Dynamic Treatment of Liquid in Motion?

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SUMMARY

The maximum capillary rise of a liquid is determined by the formula 2σ/(ρgr), where σ represents surface tension, ρ is the liquid density, g is the acceleration due to gravity, and r is the radius of the capillary. This formula applies under the assumption of an infinite surrounding reservoir. However, when considering a narrower surrounding, the dynamics of the liquid in motion must be taken into account for accurate calculations. The discussion emphasizes the importance of precise language in problem statements to avoid misinterpretation.

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Rituraj131
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Homework Statement
A capillay tube is just in contact with a liquid surface of perfectly wetting liquid. What is the maximum height liquid can rise inside the capilary?
Relevant Equations
H=2σcos(θ)/(ρgr)
I know that the height in general is goven by 2σcos(θ)/(ρgr). So the maximum height can be 2σ/(ρgr) with cos(θ)=1. But the answer given is c.
 

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Rituraj131 said:
I know that the height in general is goven by 2σcos(θ)/(ρgr).
That is for the case where the surrounding reservoir is effectively infinite in area. How do you think it might be affected by a narrower surround?
(But I am not sure this gets to answer c.)
 
haruspex said:
That is for the case where the surrounding reservoir is effectively infinite in area. How do you think it might be affected by a narrower surround?
(But I am not sure this gets to answer c.)
Thank you for you response. Actually the problem needs a dynamic treatment of the liquid in motion
 
Rituraj131 said:
Thank you for you response. Actually the problem needs a dynamic treatment of the liquid in motion
Ah, ok... you unintentionally altered the statement by writing "is just in contact" instead of "is put in contact".

Does this mean you now get the intended answer?
 
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