#### 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.

#### Solution 1

10.5 m

Density of mercury, *ρ*_{1} = 13.6 × 10^{3} kg/m^{3}

Height of the mercury column, *h*_{1} = 0.76 m

Density of French wine, *ρ*_{2} = 984 kg/m^{3}

Height of the French wine column = *h*_{2}

Acceleration due to gravity, g = 9.8 m/s^{2}

The pressure in both the columns is equal, i.e.,

Pressure in the mercury column = Pressure in the French wine column

`rho_1h_1g = rho_2h_2g`

`h_2 = (rho_1h_1)/rho_2`

`= (13.6xx10^3xx0.76)/984`

= 10.5 m

Hence, the height of the French wine column for normal atmospheric pressure is 10.5 m

#### Solution 2

We know that atmospheric pressure, `P = 1.01 xx 10^5 "Pa"`

If we use French wine of density, `rho= 984 kg m^(-3)`, then height of wine column should be

`h_(m')` such that `p = hrhog`

`=> h_m = P/(rhog) = (1.01xx10^5)/(984xx9.8) = 10.47m ~~10.5 m`