Question

Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density $984kg{m}^{–3}$ . Determine the height of the wine column for normal atmospheric pressure.

Answer 1

Density of mercury, ${\rho }_1=13.6\times {10}^{3}kg/m^3$
Height of the mercury column, h${}_1=0.76m$
Density of French wine, ${\rho }_2=984kg/m^3$
Height of the French wine column = $h_2$
Acceleration due to gravity, $g=9.8m/s^2$
The pressure in both the columns is equal, i.e.,
Pressure in the mercury column = Pressure in the French wine column
${\rho }_1{h}_{1}g={\rho }_2{h}_{2}g{h}_2=\frac{{\rho }_1{h}_1}{{\rho }_2}=\frac{13.6\times {10}^3\times 0.76}{984}$ = 10.5 m
Hence, the height of the French wine column for normal atmospheric pressure is 10.5 m.