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 and Explanation
10.5 m Density of mercury, ρ1 = 13.6 × 10 3 kg / m3
Height of the mercury column, h1 = 0.76 m
Density of French wine, ρ2 = 984 kg/m3
Height of the French wine column = h2
Acceleration due to gravity, g = 9.8 m/s2
The pressure in both the columns is equal, i.e.,
Pressure in the mercury column = Pressure in the French wine column
ρ1h1g = ρ2h2g
\(h_2 = \frac{ρ_1h_1 }{ ρ_2}\)
\(=\frac{ 13.6 × 10 3 × 0.76 }{ 984 }\)
= 10.5 m
Hence, the height of the French wine column for normal atmospheric pressure is 10.5 m.
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Concepts Used:
Bernauli Theorem
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738.
