Capillary action: mercury depression

In summary, The question asks for the internal diameter of a capillary inserted into a pool of mercury with a depressed height of 1.6cm. The equation for capillary depression is used, which is the same as capillary rise except the cohesive force is greater than the adhesive force. The given values of surface tension, contact angle, height of depression, and density of mercury can be used to calculate the internal radius and then the internal diameter of the capillary."
  • #1
lovegood
6
0
hi guys, need some help for this question.

a capillary of unknown internal radius was inserted into a pool of mercury into a pool of mercury. the height of mercury within the capillary was depressed 1.6cm below the free liquid. Calculate the internal diameter of the capillary. For the mercury-air interface on glass, the contact angle is 140 degree. for mercury at 298.15K, density= 13.59g/cm3, surface tension=0.4865Nm-1

im not sure how to go about solving this question. is it the same approach for capillary rise, but in this case it's a depression, which is due to the cohesive force being greater than the adhesive force. for capillary rise, 2 x pi x r x surface tension x cos angle = pi x r2 x h x density x g.
 
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  • #2
Yes, the same approach for capillary rise can be used to solve this problem. The equation for capillary depression is: 2πr SurfaceTensionCosθ = πr2h(ρg) where ρ is the density and g is the acceleration due to gravity. In this case, you can use the given values of surface tension and contact angle as well as the given height of depression and density of mercury to solve for the internal radius of the capillary. Then you can calculate the internal diameter by multiplying the internal radius by two.
 

1. What is capillary action?

Capillary action is the movement of a liquid through a narrow space or tube due to the forces of adhesion, cohesion, and surface tension.

2. How does capillary action work?

Capillary action occurs when the adhesive forces between the liquid and the surface it is in contact with are stronger than the cohesive forces within the liquid. This causes the liquid to rise or fall in a narrow space, such as a thin tube or small pores in a material.

3. What is mercury depression in capillary action?

Mercury depression is a phenomenon where the surface tension of mercury is lowered when it is in contact with a solid surface, causing it to spread out and form a concave shape. This is due to the strong adhesive forces between mercury and most solid surfaces.

4. Why is mercury often used to demonstrate capillary action?

Mercury is a commonly used liquid to demonstrate capillary action because it has a very high surface tension and low cohesion, making it easy to observe the movement of the liquid in a narrow space. Additionally, the low cohesive forces make it less likely for the liquid to stick to the surface it is in contact with, allowing for a clearer demonstration of capillary action.

5. What are some applications of capillary action?

Capillary action has many practical applications, such as in plants where it helps with the movement of water from the roots to the leaves. It is also used in paper towels and sponges to absorb and hold liquids. In addition, it is utilized in microfluidic devices, such as lab-on-a-chip technology, and in medical devices such as blood glucose test strips.

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