First slide

Pressure in a fluid-mechanical properties of fluids

Question

A vertical U-tube of uniform cross-section contains mercury in both sides of its arms as shown below.
Glycerin column of 10 cm is introduced into one of its arms. Oil of density 0.8 g/cc is poured into the other arm until the upper surface of the oil and glycerin are at the
same horizontal level.
$[ρ_{Hg} = 13.6 g / cc, ρ_{glycerine} = 1.3 g / cc]$
The length of oil column is

Moderate

A

10.4 cm
B

8.2 cm
C

7.2 cm
D

9.6 cm

Solution

$P_{A} = P_{B} \Rightarrow P_{0} + ρ_{glycerine} g \times 10 = P_{0} + ρ_{oil} \times g \times h + ρ_{Hg} \times g \times (10 - h)$
$\Rightarrow 1.3 \times 10 = 0.8 \times h + 13.6 \times 10 - 13.6 h$
$\Rightarrow 12.8 h = 12.3 \times 10 \Rightarrow h = 9.6 cm$

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