Question

В цилиндрическом сосуде находятся равные по массе разнородные жидкости ртуть и вода. Общая высота столба жидкостей Н. Определить давление на дно сосуда. Плотность воды Рв, плотность ртути Рр

Answer 1

M(р)=m(в); S - площадь дна сосуда
m=p*V=p*S*h
p(p)*S*h(р)=p(в)*S*h(в); h(в)=p(p)*h(р)/p(в)
H=h(р)+h(в)=h(р)*(1+p(p)/p(в))
h(р)=Н/(1+p(p)/p(в))
h(в)=Н*p(p)/(p(в)*(1+p(p)/p(в)))
P=P1+P2=p(p)*h(р)*g+p(в)*h(в)*g
Дальше расписывать не буду так как смысл понятен, величины выражены через имеющиеся.

Answer 2

Calculation of Pressure at the Bottom of the Cylinder

To determine the pressure at the bottom of the cylindrical vessel containing two different liquids, mercury and water, we can use the hydrostatic pressure formula. The hydrostatic pressure is given by the equation:

P = ρgh

Where: - P is the pressure at a certain depth - ρ is the density of the liquid - g is the acceleration due to gravity - h is the height of the liquid column

In this case, we have two liquids, mercury and water, with different densities. Let's denote the density of water as ρw and the density of mercury as ρm.

The total height of the liquid column, H, is given in the problem statement.

To calculate the pressure at the bottom of the vessel, we need to consider the pressure contribution from both liquids. Let's denote the pressure at the bottom of the vessel as Pb.

We can split the total height H into two parts: the height of the water column, Hw, and the height of the mercury column, Hm.

Since the liquids are in equilibrium, the pressure at the bottom of the vessel is the same for both liquids. Therefore, we can write:

Pb = Pw = Pm

Using the hydrostatic pressure formula for each liquid, we have:

Pw = ρw * gw * Hw Pm = ρm * gm * Hm

Where: - gw is the acceleration due to gravity for water - gm is the acceleration due to gravity for mercury

Since the liquids are in the same vessel, the height of the water column and the height of the mercury column add up to the total height:

Hw + Hm = H

Now, let's substitute the values into the equations and solve for the pressure at the bottom of the vessel.

Calculation Steps:

1. Substitute the values into the equation for the pressure of water: Pw = ρw * gw * Hw

2. Substitute the values into the equation for the pressure of mercury: Pm = ρm * gm * Hm

3. Since the pressure at the bottom of the vessel is the same for both liquids, we have: Pb = Pw = Pm

4. Substitute the values into the equation for the total height: Hw + Hm = H

5. Solve the equations simultaneously to find the pressure at the bottom of the vessel, Pb.

Let's proceed with the calculations.

Calculation:

Given: - Density of water (ρw) =- Density of mercury (ρm) =- Total height of the liquid column (H) = Substituting the values into the equations:

Pw = ρw * gw * Hw Pm = ρm * gm * Hm Pb = Pw = Pm Hw + Hm = H

We need to know the values of the acceleration due to gravity for water (gw) and mercury (gm). These values are not provided in the question. Could you please provide the values of gw and gm?