Question

Высота столба керосина в сосуде 10 см. какой должна быть высота столба воды, налитой вместо керосина, чтобы давление на дно осталось прежним?

Answer 1

P1=ρ1*g*h1

p2=ρ2*g*h2

По условию:
p1 = p2
ρ*h1=ρ2*h2

h2 = ρ1*h1 / ρ2 = 800*0,1 / 1000 = 0,08 м = 8 сантиметров

Answer 2

Давление столба жидкости на дно сосуда:
$p=\rho_{kerosin}gh_{kerosin}\\p=\rho_{H_20}gh_{H_20}\\\rho_{kerosin}gh_{kerosin}=\rho_{H_2 0}gh_{H_2 0}\\h_{H_20}=\frac{\rho_{kerosin}h_{kerosin}}{\rho_{H_2 0}};\\h_{H_2 0}=\frac{800*0.1}{1000}=0.08 m=8 sm$

Answer 3

Calculating the Height of Water Column to Maintain Pressure

To calculate the height of the water column needed to maintain the same pressure as the kerosene column, we can use the principle that the pressure at the bottom of a fluid column is determined by the height and density of the fluid above it.

Given: - Height of the kerosene column = 10 cm

We need to find the height of the water column that would exert the same pressure at the bottom of the vessel.

Solution:

The pressure at the bottom of the vessel is determined by the height and density of the fluid column above it. The pressure is given by the formula:

P = ρgh

Where: - P = pressure - ρ = density of the fluid - g = acceleration due to gravity - h = height of the fluid column

To maintain the same pressure at the bottom of the vessel, the pressure due to the water column should be equal to the pressure due to the kerosene column.

Calculating the Height of Water Column:

The density of kerosene is approximately 820 kg/m³, and the density of water is approximately 1000 kg/m³. The acceleration due to gravity, g, is approximately 9.81 m/s².

Using the formula P = ρgh, we can calculate the height of the water column as follows:

For kerosene: - Density (ρ) = 820 kg/m³ - Height (h) = 10 cm = 0.1 m - Acceleration due to gravity (g) = 9.81 m/s²

P_kerosene = 820 * 9.81 * 0.1

For water: - Density (ρ) = 1000 kg/m³ - Height (h) = ? - Acceleration due to gravity (g) = 9.81 m/s²

P_water = 1000 * 9.81 * h

Setting the pressures equal to each other: 820 * 9.81 * 0.1 = 1000 * 9.81 * h

Solving for h: h = (820 * 9.81 * 0.1) / (1000 * 9.81)

Result:

h ≈ 0.0837 m

So, the height of the water column that needs to be poured into the vessel to maintain the same pressure at the bottom is approximately 8.37 cm.

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