Question

Torricelli'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

when in Toricelli's barometer mercury is used
Density of mercury , $\rho_{hg}$ = 13.6 × 10³ kg/m³
Height of mercury column at atmospheric pressure , h = 0.76 m

when in Torricelli barometer French wine is used.
Density of French wine , $\rho_F$= 984 kg/m³
Height of the French wine column at atmospheric pressure = $h_F$

We know that pressure in a column of height h and density ρ = ρgh

Pressure in both the columns is the same i.e. atmospheric pressure

$\rho_{hg}gh=\rho_Fgh_F$

or, 13.6 × 10³ kg/m³ × 0.76m = 984 kg/m³ × $h_F$

$h_F=\frac{13600\times7.6}{984}=10.504$

Hence the height of French white column at normal atmospheric pressure is 10.504 m.

Answer 2

Hey mate,

◆ Answer - 10.5 m

◆ Explanation-
# Given-
ρ = 13600 kg/m^3
h = 0.76 m
ρ' = 984 kg/m^3
h' = ?

# Solution -
Pressure measured by mercury barometer,
P = ρhg

Pressure measured by french wine barometer,
P' = ρ'h'g

But here, both barometers measure normal atmosperic pressure.
P = P'
ρhg = ρ'h'g
h' = ρh / ρ'
h' = 13600×0.76 / 984
h' = 10.5 m

Thus french wine barometer will show a reading of 10.5 m

Hope that was useful...