Question

Container is filled with mercury to a depth of 10 cm. On top of the mercury floats a 40cm thick layer of water with a density of 1x10^3kg/m^3.if know the density of mercury is 13.6x10^3kg/m^3. g=9.81m/s^2.

a) What hat is the pressure at the surface of this water?
b)what is the absolute pressure at the bottom of the container?

Answer 1

The pressure at the surface of the water is 105,245 Pa, which is the sum of the pressure due to the water column and the atmospheric pressure. The absolute pressure at the bottom of the container is 118,613 Pa, which is the sum of the pressure due to the water column, the pressure due to the mercury column, and the atmospheric pressure.

Step-by-step explanation:

To find the pressure at the surface of the water, we need to consider the pressure due to the water column and the atmospheric pressure.

The pressure due to the water column can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height of the water column. In this case, h is 40 cm and the density of water is 1x10^3 kg/m^3, which gives us a pressure due to the water column of P = (1x10^3 kg/m^3)(9.81 m/s^2)(0.4 m) = 3920 Pa.

The atmospheric pressure is approximately 101,325 Pa.

So, the pressure at the surface of the water is the sum of the pressure due to the water column and the atmospheric pressure:

P = 3920 Pa + 101,325 Pa = 105,245 Pa.

For the absolute pressure at the bottom of the container, we need to consider the pressure due to the water column, the pressure due to the mercury column, and the atmospheric pressure.

Using the same formula as before, the pressure due to the water column is P = (1x10^3 kg/m^3)(9.81 m/s^2)(0.4 m) = 3920 Pa.

The pressure due to the mercury column can be calculated in a similar way, using the density of mercury, which is 13.6x10^3 kg/m^3, and the height of the mercury column, which is the difference between the total depth of the container (10 cm) and the height of the water column (40 cm):

P = (13.6x10^3 kg/m^3)(9.81 m/s^2)(0.1 m) = 13,368 Pa.

The atmospheric pressure is approximately 101,325 Pa.

So, the absolute pressure at the bottom of the container is the sum of the pressure due to the water column, the pressure due to the mercury column, and the atmospheric pressure:

P = 3920 Pa + 13,368 Pa + 101,325 Pa = 118,613 Pa.