The cylindrical vessel contains mercury and water. The mass of mercury is equal to the mass of water.

The cylindrical vessel contains mercury and water. The mass of mercury is equal to the mass of water. The total height of the two layers of liquid is 29.2 cm. Calculate the pressure at the bottom of this vessel.

The height of the column of mercury is x, the area of the base of the cylinder is S.

Water column height:
0.292 m – x.

Mercury volume:

Vр = Sx.

Mercury mass:

mр = ρрVр = ρрSx (ρр is the density of mercury).

Similarly, we find the mass of water:

mw = ρwVw = ρwS (0.292 m – x) (ρw is the density of water).

mр = mv;

ρрSx = ρвS (0.292 m – x);

ρрx = ρv (0.292 m – x);

ρрx + ρвx = ρв * 0.292 m;

x = (ρw * 0.292 m) / (ρw + ρw) =
= (1000 kg / m ^ 3 * 0.292 m) / (1000 kg / m ^ 3 + 13600 kg / m ^ 3) =
= 0.02 m.

The pressure is equal to the sum of the pressures of mercury and water:

P = ρрgx + ρвg (0.292 m – x) = 10 m / s ^ 2 * (13600 kg / m ^ 3 * 0.02 m + 1000 kg / m ^ 3 * 0.272 m) = 5440 N / m ^ 2.

Answer: 5.44 kPa.