A column of water in communicating vessels 8.6 cm high balances a column of kerosene 10 cm high.

A column of water in communicating vessels 8.6 cm high balances a column of kerosene 10 cm high. Find the density of the kerosene.

Given:

l1 = 8.6 centimeters = 0.086 meters – the height of the water column in the communicating vessels (left knee);

ro1 = 1000 kg / m3 (kilogram per cubic meter) – water density;

l2 = 10 centimeters = 0.1 meter – the height of a column of kerosene in communicating vessels (right knee).

It is required to determine ro2 (kg / m3) – the density of kerosene.

According to the law of communicating vessels, the pressure in the left knee will be equal to the pressure in the right knee. Then:

P1 = P2;

ro1 * l1 * g = ro2 * l2 * g, where g = 9.8 Newton / kilogram;

ro1 * l1 = ro2 * l2, from here we find that:

ro2 = ro1 * l1 / l2 = 1000 * 0.086 / 0.1 = 86 / 0.1 = 860 kg / m3.

Answer: the density of kerosene is 860 kg / m3.