Maximum Capillary Rise: Dynamic Treatment of Liquid in Motion?

In summary, the maximum height of a liquid in motion is given by 2σcos(θ)/(ρgr) when the surrounding reservoir is effectively infinite in area. However, if the surrounding reservoir is narrower, this may affect the maximum height. The problem may require a dynamic treatment of the liquid in motion, as unintentional alterations in the statement can lead to different answers.
  • #1
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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  • #2
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.)
 
  • #3
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
 
  • #4
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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1. What is maximum capillary rise?

Maximum capillary rise is the maximum height that a liquid can rise in a narrow tube due to capillary action. It is influenced by factors such as the surface tension, density, and viscosity of the liquid, as well as the size and shape of the tube.

2. How is maximum capillary rise measured?

The maximum capillary rise can be measured by placing a narrow tube in a liquid and observing the height to which the liquid rises. This can also be calculated using the Young-Laplace equation, which takes into account the properties of the liquid and the tube.

3. What are the applications of maximum capillary rise?

Maximum capillary rise has several practical applications, including in the medical field for measuring blood pressure, in oil exploration for determining the permeability of rock formations, and in materials science for studying the properties of porous materials.

4. How does surface tension affect maximum capillary rise?

Surface tension is a major factor that influences maximum capillary rise. A higher surface tension results in a higher maximum capillary rise, as it allows the liquid to overcome gravity and adhere to the walls of the tube more strongly.

5. Can maximum capillary rise be changed?

Yes, maximum capillary rise can be changed by altering the properties of the liquid or the tube. For example, using a liquid with a lower surface tension or a wider tube can result in a lower maximum capillary rise. Additionally, external factors such as temperature and pressure can also affect maximum capillary rise.

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