Liquid in a vertical pipe open at the lower end and closed at the top

In summary, the stability of the meniscus is key in determining whether or not liquid will fall out of a vertical pipe. In a small diameter pipe, a stable meniscus will form due to surface tension, preventing the liquid from falling out. However, in a larger diameter pipe, the surface tension may not be strong enough to create a stable meniscus, causing the liquid to fall out. This is known as the Rayleigh-Taylor instability and can be explained in detail in the textbook "Physics of continuous matter" by B. Lautrup. The critical diameter for a tube with air and water is 8.5 mm.
  • #1
anders_r_r
5
0
Consider a vertical pipe partially filled with liquid. The pipe is open at the lower end and closed at the top. See the attached picture. Will the liquid fall out or not?

In a small diameter pipe a stable meniscus will form due to surface tension and prevent the water from falling out. In a larger diameter pipe the liquid will fall out of the pipe. What is the exact criterion that determines wether or not the water will fall out? Where/how do I find the answer? Can someone point me in the right direction?

/Anders
 

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  • #2
I suppose it depends on what liquid. Perhaps its viscosity, but maybe also other properties it may have.
 
  • #3
Thanks for your input, Dr Lots-o'watts.

I suppose that the answer is closely related to the stability of the meniscus. In a large pipe the surface tension may not be strong enough to create a stable meniscus.
 
  • #4
After a few days of searching I found the answer :-)

In the large diameter tube long wavelength capillary waves on the interface between the gas and liquid causes the interface to be unstable and the liquid will fall out. This phenomena is called the Rayleigh-Taylor instability.

When the diameter of the tube is sufficiently small, the longest possible wavelength of the capillary waves is not long enough to cause instablity, thus the liquid will stay in the tube.

If the gas is air and the liquid is water, the critical diameter of the tube is 8.5 mm.

The theory is very well explained in the textbook: "Physics of continuous matter" by B. Lautrup.
 
  • #5


The exact criterion that determines whether or not the liquid will fall out of the vertical pipe is the balance between the gravitational force pulling the liquid downward and the surface tension force keeping the liquid from falling out. This balance is known as the capillary action.

To find the answer, you can look into the equations for capillary action and the parameters that affect it, such as the surface tension of the liquid, the diameter of the pipe, and the density of the liquid. Additionally, you can also conduct experiments to observe the behavior of liquids in different pipe sizes and conditions.

Some helpful resources for understanding capillary action and its criteria include textbooks on fluid mechanics and surface tension, as well as scientific articles and research papers on the topic. You can also consult with experts in the field of fluid mechanics or conduct further research through online databases or scientific organizations.
 

FAQ: Liquid in a vertical pipe open at the lower end and closed at the top

What is the purpose of a vertical pipe open at the lower end and closed at the top?

A vertical pipe open at the lower end and closed at the top is used for transporting liquids from a lower elevation to a higher elevation. It can also be used for measuring the pressure at different depths within the liquid.

How does the liquid flow through a vertical pipe?

The liquid in a vertical pipe flows due to the difference in pressure between the bottom and top of the pipe. The pressure at the bottom is higher due to the weight of the liquid above it, causing the liquid to flow upwards towards the lower pressure at the top of the pipe.

What factors affect the flow rate of liquid in a vertical pipe?

The flow rate of liquid in a vertical pipe is affected by the diameter of the pipe, the viscosity of the liquid, the length of the pipe, and the pressure difference between the top and bottom of the pipe.

How does the density of the liquid affect the pressure at different depths in the pipe?

The pressure at different depths in a vertical pipe is directly proportional to the density of the liquid. This means that the pressure will increase with depth as the density of the liquid increases.

Can the flow rate of liquid in a vertical pipe be controlled?

Yes, the flow rate of liquid in a vertical pipe can be controlled by adjusting the pressure difference between the top and bottom of the pipe, as well as the diameter and length of the pipe. This can be achieved through the use of valves or pumps.

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