A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit ?
Solution and Explanation
The given system of water, mercury, and methylated spirit is shown as follows :
Height of the spirit column, h1 = 12.5 cm = 0.125m
Height of the water column, h2 = 10 cm = 0.1 m
P0 = Atmospheric pressure
ρ1 = Density of spirit
ρ2 = Density of water
Pressure at point B = P0 + h1ρ1g
Pressure at point D = P0 + h2ρ2g
Pressure at points B and D is the same.
P0 + h1ρ1g = h2ρ2g
\(= \frac{ρ_1 }{ ρ_2} = \frac{h_2 }{ h_1} \)
\(=\frac{ 10 }{ 12.5 }= 0.8\)
Therefore, the specific gravity of spirit is 0.8.
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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.
