Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

Statement

$1.2.10.$ 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?

Solution

Let's use the Method of Dimensions

$$[q] = \frac{m^3}{s \cdot m^2} \Leftrightarrow [q] = \frac{m}{s}$$

What corresponds to

$$t = R/q$$

As the radius of the aquarium increases, water flows out slower, and the opposite is true as $q$ increases.

Answer

$$t = \frac{R}{q}$$