The U-shaped vessel contains water. A column of kerosene 10 cm high was poured into the left knee.

The U-shaped vessel contains water. A column of kerosene 10 cm high was poured into the left knee. Kerosene does not mix with water. 1 What is the difference in fluid levels in the knees? 2 Where will the liquid level be higher on the left or right?

Given:

h1 = 10 centimeters = 0.1 meters – the level of a column of kerosene, which was poured into a U-shaped tube in the left knee;

g = 10 Newton / kilogram – acceleration of gravity;

ro1 = 800 kilograms / cubic meter – density of kerosene;

ro2 = 1000 kilograms / cubic meter – density of water.

It is required to determine dh (meter) – the difference in levels in the left and right knees, as well as in which knee the liquid level will be higher.

According to the law of communicating vessels, the pressure created by the water column with the level h1 on the left side of the tube will be equal to the pressure created by the level of mercury h2 on the right side of the tube:

P1 = P2;

ro1 * g * h1 = ro2 * g * h2;

ro1 * h1 = ro2 * h2;

h2 = ro1 * h1 / (ro2) = 800 * 0.1 / 1000 = 80/1000 = 8/100 = 0.08 meters.

Then:

dh = h1 – h2 = 0.1 – 0.08 = 0.02 meters.

Since h1> h2, the level in the left knee will be higher.

Answer: the level difference will be 0.02 meters, the level in the left knee will be higher.