Question

Які розміри повинні мати капіляри дерева, щоб підняти воду на висоту 30 м - висоту середньої сосни? Яку роботу при цьому виконують сили поверхневого натягу?

Answer 1

h = 2σ/(ρgr); r = 2σ/(ρgh) = 72·10⁻³/(1000·10·30) = 24 · 10⁻⁸ м;

А = (Fh)/2 = (σ2πrgh)/2 = σπrgh = 72·10⁻³· 3.14 · 24 · 10⁻⁸ · 10 · 30 =

=16277,76 · 10⁻⁹Дж = 16277,76 нДж

Answer 2

Size of Capillaries in Trees and the Forces of Surface Tension

To understand the size of capillaries in trees required to lift water to a height of 30 meters, we need to consider the forces of surface tension and the properties of water transport in plants.

Capillary Size in Trees: Capillaries in trees, also known as xylem vessels, are responsible for transporting water from the roots to the leaves. These vessels are microscopic in size and vary in diameter depending on the tree species. The average diameter of xylem vessels in coniferous trees, such as pine trees, ranges from 10 to 100 micrometers.

Water Transport in Trees: Water is transported in trees through a process called transpiration. Transpiration is the evaporation of water from the leaves, which creates a negative pressure or tension in the xylem vessels. This negative pressure pulls water up from the roots to the leaves, against the force of gravity.

Forces of Surface Tension: Surface tension is the cohesive force between water molecules at the air-water interface. It is responsible for the curved shape of water in capillary tubes and the ability of water to rise in narrow tubes against gravity.

When water enters the capillaries in trees, the forces of surface tension allow it to adhere to the inner walls of the vessels and rise upwards. The narrower the capillary, the higher the water can be lifted due to increased surface tension.

Work Done by Surface Tension: The forces of surface tension play a crucial role in lifting water in capillaries. As water rises in the capillaries, the surface tension forces act to overcome the gravitational force pulling the water downwards. This work done by surface tension allows water to be transported to great heights in trees.

However, it is important to note that the forces of surface tension alone are not sufficient to lift water to a height of 30 meters in a tree. Other factors, such as the cohesion and adhesion properties of water, as well as the structure and function of the xylem vessels, also contribute to the upward movement of water.

In conclusion, the size of capillaries in trees required to lift water to a height of 30 meters, the height of an average pine tree, can vary depending on the tree species. The forces of surface tension, along with other factors, enable water to be transported against gravity in trees.