The density of mercury #(13593 (kg)/m^3)# is much more than that of ethanol#(789(kg)/m^3)# and water #(1000 (kg)/m^3)#. What this means is that height of mercury required to produce a given pressure is much less than the height of a column of water or ethanol.
Let's do a simple calculation to illustrate the point.
The pressure a manometer normally measures is of the order of atmospheres. #1 atmosphere = 10^5Pa# in SI units.
Now, #dgh = P# #=> h=P/(dg)# where
#P# = pressure
#d# = density of material used
#g# = acceleration due to gravity. Let us take it as #10m/s^2# for simplicity.
#h # = height of column
#therefore# height of mercury column required to produce/measure a pressure of #1atm = 10^5Pa# is:-
#100000/(13593*10) approx 0.735m = color(red)(73.5 cm)#
Similarly height of water column for #1atm = 10^5Pa# is:-
#100000/(1000*10) = 10m = color(red)(1000cm)#
and for ethanol is:-
#100000/(789*10) approx 12.67m = color(red)(1267cm) #
Now you can easily see that the height of mercury column required i.e. #73.5 cm# is much more feasible to use than heights of #1000cm# or #1267cm#.
