Question

В дне сосуда имеется маленькое отверстие диаметром 0,5 мм. До уровня какой высоты можно налить воду в сосуд, чтобы она не вытекала через отверстие?

Answer 1

Объяснение:

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Answer 2

Calculating the Height of Water in the Vessel

To calculate the height of water in the vessel such that it does not leak through the small hole, we can use the principle of hydrostatics. The pressure at the bottom of the vessel must be greater than the pressure at the hole to prevent the water from leaking.

The formula to calculate the pressure at a certain depth in a liquid is given by:

P = ρgh

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

The pressure at the hole can be calculated using this formula, and it should be greater than the atmospheric pressure to prevent leakage.

Using the Given Diameter of the Hole

The diameter of the hole is given as 0.5 mm. We can use this information to calculate the velocity of the water coming out of the hole using the Torricelli's law, which states that the velocity of fluid flowing out of an orifice is given by:

v = √(2gh)

Where: - v = velocity of the fluid - g = acceleration due to gravity - h = height of the liquid column

By equating the pressure at the hole to the atmospheric pressure and using the velocity of the water coming out of the hole, we can calculate the height of the water column in the vessel.

Conclusion

By using the principles of hydrostatics and Torricelli's law, we can calculate the height of the water column in the vessel such that it does not leak through the small hole. This height can be determined by considering the pressure at the hole and the velocity of the water coming out of it.

Please note that the specific calculations for the height of the water column would depend on the exact values of the density of the liquid and the acceleration due to gravity, which are not provided in the given question.