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| <h2>Solutions of Savchenko Problems in Physics</h2> | | <h2>Solutions of Savchenko Problems in Physics</h2> |
| <p class="author"> | | <p class="author"> |
| Aliaksandr Melnichenka <br/> | | Aliaksandr Melnichenka <br/> |
| October 2023 | | October 2023 |
| $1.2.10.$ From a hemispherical aquarium of radius $R$ filled with water, a volume of liquid $q$ evaporates from a unit of the water surface per unit of time. How long will it take for the water to evaporate? | | $1.2.10.$ From a hemispherical aquarium of radius $R$ filled with water, a volume of liquid $q$ evaporates from a unit of the water surface per unit of time. How long will it take for the water to evaporate? |
| </p> | | </p> |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
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| <p> | | <p> |
| Let's use the Method of Dimensions | | Let's use the Method of Dimensions |
| </p> | | </p> |
| <p class="exp"> | | <p class="exp"> |
| $$[q] = \frac{m^3}{s \cdot m^2} \Leftrightarrow [q] = \frac{m}{s}$$ | | $$[q] = \frac{m^3}{s \cdot m^2} \Leftrightarrow [q] = \frac{m}{s}$$ |
| </p> | | </p> |
| | | |
| <p> | | <p> |
| What corresponds to | | What corresponds to |
| </p> | | </p> |
| <p> | | <p> |
| $$t = R/q$$ | | $$t = R/q$$ |
| </p> | | </p> |
| <p> | | <p> |
| As the radius of the aquarium increases, water flows out slower, and the opposite is true as $q$ increases. | | As the radius of the aquarium increases, water flows out slower, and the opposite is true as $q$ increases. |
| </p> | | </p> |
| </p> | | </p> |
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| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| $$t = \frac{R}{q}$$ | | $$t = \frac{R}{q}$$ |
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