In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury = 13.6)
Solution and Explanation
Height of the water column, h1 = 10 + 15 = 25 cm
Height of the spirit column, h2 = 12.5 + 15 = 27.5 cm
Density of water, ρ1 = 1 g cm-3
Density of spirit, ρ2 = 0.8 g cm-3
Density of mercury = 13.6 g cm-3
Let h be the difference between the levels of mercury in the two arms.
Pressure exerted by height h, of the mercury column :
= hρg = h × 13.6 g ...(i)
Difference between the pressures exerted by water and spirit :
= h1ρ1g - h1ρ1g
= g(25 × 1 – 27.5 × 0.8)
= 3g … (ii)
Equating equations (i) and (ii), we get :
13.6 hg = 3g
h = 0.220588 ≈ 0.221 cm
Hence, the difference between the levels of mercury in the two arms is 0.221 cm.
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Concepts Used:
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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.
