Fluid mechanics barometer problem

[anmolnanda]

to construct a barometer,a tube of length 1m is filled completely with mercury and is inverted in a mercury cup.the barometer reading on a particular day is 76cm.suppose a 1m tube is filled with mercury upto 76cm and then closed by a cork.It is inverted in a mercury cup and the cork is removed.Height of mercury column in the tube over the surface is
<76cm
why??
i want to know why it is <76cm as the books did not explain this

 

[JaredJames]

If it is filled completely, when you invert it the weight of the mercury is counteracted by the atmospheric pressure pushing down on the fluid in the cup (I assume you know how a barometer works).

So the fluid level drops until the weight of the fluid in the tube = the force of the atmospheric pressure. As the fluid level drops, it leaves a vacuum in above it in the tube.

Now, when you only fill it to 76cm there is air remaining in the tube at atmospheric pressure. This means that you have the weight of the mercury acting plus the force applied by this air at atmospheric pressure.

You still only have the atmospheric pressure acting on the fluid in the cup as above, so this force now has to equal the weight of the mercury plus the force applied by the air inside the tube. Because the force from the internal air is constant, the mercury level has to be lower. (Mercury level is lower which means overall weight of mercury is less. This weight plus the atmospheric air = external air pressure.)