In a U-shaped tube (a tube shaped like the Latin letter U) of constant cross-section, there is mercury.

In a U-shaped tube (a tube shaped like the Latin letter U) of constant cross-section, there is mercury. Determine the level of rise of mercury relative to the initial level on the right side of the tube, if water is poured into the left side so that it forms a pillar with a height of h = 13.6 cm.

Given:

h1 = 13.6 centimeters = 0.136 meters – the level of the water column, which was poured into the U-shaped tube;

g = 10 Newton / kilogram – acceleration of gravity;

ro1 = 1000 kilograms / cubic meter – density of water;

ro2 = 13600 kilograms / cubic meter – the density of mercury.

It is required to determine h2 (meter) – how much the level of mercury has risen relative to its initial level in the right tube.

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) = 1000 * 0.136 / 13600 = 136/13600 = 1/100 = 0.01 meter.

Answer: The level of mercury has risen by 0.01 meters (1 centimeter).