Question

in a U-tube barometer, mercury (or some other fluid) is placed in a U shaped tube. The air is vacuumed out of one end, which is then sealed. Atmospheric pressure pushes down on the other end, resulting in the two surface levels being at different heights. If we made a U-tube barometer using olive oil as our fluid, how tall would we need to make it to be able to measure standard atmospheric pressure? Based on this answer, why do you think we use mercury instead when mercury is so dangerous to handle?

Answer 1

From the pressure difference formula, the pressure at the vacuum is zero. So, there will be a liquid column of height H relative to the right arm of the U-tube. And so, the atmospheric pressure can be measured from the length of the liquid column in the in the sealed end. So, we get
  

So, for olive oil, we need the the arm length to be
  
This is quite huge more than the height of the celing of a room.
For mercury the density is, \rho =13.6 gm/cm^3 . So, we get for mercury the height of the liquid column is
  
The density of mercury is very large so, the length of the mercury column corresponding to atmospheric pressure is 76 cm. This is why we use mercury instead of any other liquid.