What is the relationship between surface tension and forces?

In summary, the equilibrium of forces is a way to calculate the tension in a liquid using the law of hydrostatic pressure.
  • #1
arhzz
266
52
Homework Statement
Determine the surface tension γ of a liquid with the help of the capillary effect. The capillary has an inner diameter of 0.5 mm and the liquid with a density of 875 kg / m3 rises 3.4 cm. To do this, derive the formula for γ from the equilibrium of forces
Relevant Equations
F = mg
Hello! To this I did what was recommended and this is what it looks like

$$ F = mg $$

$$ F = \rho * V * g $$

$$ F = \ rho * \pi^2 * h * g $$

Than for the surface tension I did the same thing to get an expression for F.

$$ y = \frac {F} {2 \pi r}$$
Than tried to get F out and than equate both of the equations, than F and pi would be on both sides so it would cancel out leaving me with this.

$$ \rho * r^2 *h * g = 2 * y * r $$
Than I tried to get the tension out so I moved everything accordingly and got this $$ y = \frac {h* \rho*g*r} {2}$$

The result should be 0,0365 N/m

Now the reason why I am posting this question is why is it recommened to use the equilibrium of forces? I tried to calculate the tension, with an equation that was given to us in class, it doenst include any forces and I got a whole diffrent result. I'd assume this is the right way to do it given the suggestion in the task itself but why? And in a situation where this "hint" wasnt given to me I'd never come to use this variant, id just do with the formula provided in class. Any insights?

Thank you!
 
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  • #2
Surely the formula that they gave you in class is the one of the well-known Jurín law https://en.wikipedia.org/wiki/Jurin's_law
Your derivation of the formula by means of hydrostatic equilibrium is correct, you just have to consider that the angle of the smallis formed by the liquid is zero, so the cosine becomes unity.

Your calculation result is correct 0.0365N / m
Check the Latex calculation of the area missing a "## r ##"
 
  • #3
Yes that was the formula that was given to us,And your right I am missing an "r". And taht with the cosine I didnt even think about,clears things up.

Thank you!
 

Related to What is the relationship between surface tension and forces?

1. What is surface tension?

Surface tension is the cohesive force that exists between molecules on the surface of a liquid. It is the result of the imbalance of forces between molecules at the surface and those in the bulk of the liquid.

2. How is surface tension measured?

Surface tension is typically measured in units of force per unit length, such as newtons per meter or dynes per centimeter. It can be measured using various methods, such as the drop weight method or the capillary rise method.

3. What factors affect surface tension?

Surface tension is affected by factors such as temperature, pressure, and the type of liquid. It is also influenced by the presence of impurities or surfactants, which can decrease surface tension.

4. What is the relationship between surface tension and forces?

Surface tension is the result of intermolecular forces, such as hydrogen bonding, van der Waals forces, and dipole-dipole interactions. These forces create a net inward pull on the surface molecules, resulting in the cohesive force known as surface tension.

5. How does surface tension play a role in everyday life?

Surface tension is responsible for many phenomena in our daily lives, such as the formation of droplets, the ability of insects to walk on water, and the shape of soap bubbles. It also plays a crucial role in the functioning of our lungs and the transportation of nutrients in plants.

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