Question

A U-tube contain liquid of unknown density.An oil of density 778kg/m3 is poured into one arm of the tube until the oil column is 10 cm high.The oil air interface is then 7 cm above the liquid level in the other arm of U tube.Find the density of the liquid.

Answer 1

Question#18920

A U-tube contain liquid of unknown density. An oil of density $778\,\mathrm{kg/m^3}$ is poured into one arm of the tube until the oil column is 10 cm high. The oil air interface is then 7 cm above the liquid level in the other arm of U tube. Find the density of the liquid.

Solution:

Let:

$$\rho_2 = 778\,\mathrm{kg/m^3}$$ $$H_2 = 10\,\mathrm{cm}$$ $$H_1 = 10 - 7 = 3\,\mathrm{cm}$$

$\rho_1 - ?$

According to the law of communicating vessels:

$$\frac{\rho_1}{\rho_2} = \frac{H_2}{H_1}$$ $$\rho_1 = \frac{\rho_2 H_2}{H_1} = \frac{778 \cdot 10}{3} = 2593.33\,\mathrm{kg/m^3}$$

Answer: 2593.33 kg/m³