Question

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

Answer 1

Density of mercury, ${\rho }_1=13.6\times {10}^{3}kg/m3$

Height of the mercury column, $h_1=0.76m$

Density of French wine, ${\rho }_2=984kg/m3$

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

${\rho }_1{h}_{1}g={\rho }_2{h}_{2}g$

$h_2={\rho }_1{h}_1/{\rho }_2$

$=13.6\times {10}^3\times 0.76/984=10.5m$
Hence, the height of the French wine column for normal atmospheric pressure is 10.5 m.