# Estimate surface tension

Capillary rise is a standard method to get surface tension of a liquid. The pressure in the capillary just below the surface of the liquid is \(p_0=\frac{2S\cos\theta}{r}\) where, \(p_0\) is the atmospheric pressure, \(S\) is the surface tension, \(r\) is the radius of the capillary and \(\theta\) is the contact angle. In this activity, we have used similar concept but in a different situation. If a very small hole is made at the bottom of a vessel it can stand a column of water even if it is open at the top. This is because of hanging drop at the bottom. If you assume that in equilibrium it takes shape of a hemisphere, the equation will be

\begin{align}
h\rho g=\frac{2S}{r}
\end{align}

where \(r\) is the radius of the hole, \(S\) is the surface tension, \(h\) is the height of the column of water in the vessel and \(\rho\) its density. This can be used to estimate \(S\).

You need a plastic box with a hole at the bottom, the needle with which the hole was made, a screw guage, a stand to hold the vessel at a height, another vessel to collect the falling water, a syringe, scale, soap,

- The radius of the hole can be assumed to be equal to the radius of the needle. Measure this radius using the screw gauge. Do it several times and when you are sure that you are getting the same value, write it.
- Fix the vessel in the stand and the collector vessel below it. Pour water in the vessel up to some height.
- See if water falls through the hole. If so, you can take out some water. If it does not fall, pour more water. You have to get the situation where maximum height of column is supported by the hole. Once you get approximate height, put some more water and let the water fall drop by drop. When it stop falling, you have gotten the correct height.
- Measure the height \(h\) of the water column with the scale. Calculate the surface tension of water using equation given above. Note that $\rho=1000$ kg/m
^{3}, \(g=9.8\,\mathrm{m/s^2}\), and \(S_0=0.072\,\mathrm{N/m}\). Calculate the percentage error \(\frac{S-S_0}{S_0}\times 100\).
- Dissolve little soap in water and repeat the experiment.

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