What does it mean when the height of a barometer is rising?

The heights of mercury in a barometer at the base and at the top of a mountain are $75 \, cm$ and $50 \, cm$,respectively. If the ratio of the density of mercury to the density of air is $10^4$,what is the height of the mountain?

The diagram shows a simple mercury barometer. Which of the following does not cause the height of the mercury column to vary?

Explain why water storage dam walls are thicker at the bottom.

$A$ barometer tube,containing mercury,is lowered in a vessel containing mercury until only $50 \, cm$ of the tube is above the level of mercury in the vessel. If the atmospheric pressure is $75 \, cm$ of mercury,what is the pressure at the top of the tube?

Show that the pressure produced due to a fluid column depends on the height of the fluid column and the density of the fluid.