Question

В сообщающихся сосудах находится ртуть. В один из сосудов доливают воду, а в другой – керосин. Высота столба воды 20 см. Какой должна быть высота столба керосина, чтобы уровни ртути в обоих сосудах совпадали? Плотность воды 1000 кг/м³, плотность керосина 800 кг/м³

Answer 1

Давление воды и керосина должны быть равными р1=р2. За формулой р=p'gh (p' - плотность). p'1gh1=p'2gh2. h2=p'1gh1/p'2g. h2 = 0.25м=25см

Answer 2

Calculation of the Height of the Kerosene Column

To determine the height of the kerosene column required for the levels of mercury in both vessels to coincide, we can use the principle of Pascal's law, which states that the pressure in a fluid is transmitted equally in all directions.

Given: - Height of the water column: 20 cm - Density of water: 1000 kg/m³ - Density of kerosene: 800 kg/m³

To find the height of the kerosene column, we can use the equation:

Pressure of water = Pressure of kerosene

The pressure in a fluid is given by the equation:

Pressure = Density x Gravity x Height

Let's calculate the height of the kerosene column using the above equation.

1. Calculate the pressure of water: - Density of water = 1000 kg/m³ - Gravity = 9.8 m/s² (approximate value) - Height of water column = 20 cm = 0.2 m

Pressure of water = Density of water x Gravity x Height of water column

2. Calculate the pressure of kerosene: - Density of kerosene = 800 kg/m³ - Gravity = 9.8 m/s² (approximate value) - Height of kerosene column = ? (to be determined)

Pressure of kerosene = Density of kerosene x Gravity x Height of kerosene column

3. Set the pressures equal to each other and solve for the height of the kerosene column:

Pressure of water = Pressure of kerosene

Density of water x Gravity x Height of water column = Density of kerosene x Gravity x Height of kerosene column

Simplifying the equation:

Height of kerosene column = (Density of water / Density of kerosene) x Height of water column

Substituting the given values:

Height of kerosene column = (1000 kg/m³ / 800 kg/m³) x 0.2 m

Calculating the height of the kerosene column:

Height of kerosene column = 1.25 x 0.2 m

Height of kerosene column = 0.25 m

Therefore, the height of the kerosene column should be 0.25 meters (or 25 centimeters) for the levels of mercury in both vessels to coincide.

Please note that the above calculation assumes that the pressure at the bottom of both vessels is the same, which is a reasonable assumption in this scenario.