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Liquid Inside a U-Tube

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Question

Fig(a) shows a U-tube of uniform cross-section that is open at by both ends. It is partially filled with water. Now a liquid of density is ' $d_{1}$ ' id poured into the left arm. The liquid does not mix with water. It is observed that height of liquid surface in the left arm is $2 c m$ more than the height of water surface in the right arm as shown in figure. Take density of water as $1000 k g / m^{3}$ . Find density of the liquid $d_{1}$ .

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Solution

Pressure at the partition is equal to the pressure at point horizontal levels are equal.
$P_{A} = P_{B}$
$P_{0} + P_{l} g y = P_{0} + (y - 2) g ρ_{w} P_{l} = \frac{y - 2}{y} \times ρ_{w} d_{1} = \frac{1000 (y - 2)}{y} k g / m^{3}$

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