First slide

Fluid statics

Question

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is

Difficult

A

$425 kg m^{- 3}$
B

$800 kg m^{- 3}$
C

$928 kg m^{- 3}$
D

$650 kg m^{- 3}$

Solution

Pressure at point C ,
$P_{C} = P_{a} + ρ_{water} g h_{water}$
$where h_{water} = C E = (65 + 65) mm = 130 mm$
$Pressure at point B, P_{B} = P_{a} + ρ_{oil} g h_{oil}$
$where h_{oil} = A B = (65 + 65 + 10) mm = 140 mm$
In liquid, pressure is same at same liquid level,
$\begin{array}{l} P_{B} = P_{C} \\ ρ_{oil} g h_{oil} = ρ_{water} g h_{water} \\ ρ_{oil} = \frac{130 \times 10^{3}}{140} = \frac{13}{14} \times 10^{3} = 928.57 kg m^{- 3} \end{array}$

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