Watching the flight of balloons and the movement of ships on the surface of the sea, many people ask the question: what makes these vehicles rise to the skies or keeps them on the surface of the water? The answer to this question is buoyancy. Let's consider it in more detail in the article.
Fluids and static pressure therein
Two aggregate states of a substance are called fluid: gas and liquid. The influence of any tangential force on them causes one layer of matter to shift relative to the other, that is, matter begins to flow.
Liquids and gases consist of elementary particles (molecules, atoms) that do not have a specific position in space, as, for example, in solids. They are constantly moving in different directions. In gases, this chaotic motion is more intense than in liquids. Due to this fact, fluid substances can transmit the pressure exerted on them in all directions equally (Pascal's law).
Since all directions of motion in space are equal, the total pressure on any elementary volume inside the fluid is zero.
The situation changes radically if the substance in question is placed in a gravitational field, for example, in the gravitational field of the Earth. In this case, each layer of liquid or gas has a certain weight with which it presses on the underlying layers. This pressure is called static. It increases in direct proportion to the depth h. So, in the case of a fluid with a density Ο l, the hydrostatic pressure P is determined by the formula:
P = Ο l * g * h.
Here g = 9.81 m / s 2 is the acceleration of gravity near the surface of our planet.
Each person who dived at least once several meters under the water felt hydrostatic pressure.
Next, we consider the issue of buoyancy by the example of liquids. Nevertheless, all the conclusions that will be given are also valid for gases.
Hydrostatic pressure and the law of Archimedes
We put the following simple experience. Take a body of regular geometric shape, for example, a cube. Let the side length of the cube be a. Submerge this cube in water so that its upper face is at a depth of h. What pressure does the cube have?
To answer the question posed above, it is necessary to consider the magnitude of hydrostatic pressure, which acts on each face of the figure. Obviously, the total pressure acting on all side faces will be zero (pressure on the left side will be compensated by pressure on the right). The hydrostatic pressure on the upper face will be equal to:
P 1 = Ο l * g * h.
This pressure is directed downward. The corresponding force is:
F 1 = P 1 * S = Ο l * g * h * S.
Where S is the area of ββthe square face.
The force associated with hydrostatic pressure, which acts on the lower face of the cube, will be equal to:
F 2 = Ο l * g * (h + a) * S.
Force F 2 is directed upwards. Then the resulting force will also be directed up. Its value is equal to:
F = F 2 - F 1 = Ο l * g * (h + a) * S - Ο l * g * h * S = Ο l * g * a * S.
Note that the product of the length of the edge by the area of ββthe face S of the cube is its volume V. This fact allows us to rewrite the formula as follows:
F = Ο l * g * V.
This formula of buoyancy forces suggests that the value of F does not depend on the immersion depth of the body. Since the volume of the body V coincides with the volume of the liquid V l that it displaced, we can write:
F A = Ο l * g * V l .
The buoyancy force formula F A is called the mathematical expression of Archimedes' law. It was first established by the ancient Greek philosopher in the 3rd century BC. Archimedes' law is usually formulated as follows: if the body is immersed in a fluid substance, then a force directed vertically upward acts on it, which is equal to the weight of the substance displaced by the body under consideration. The buoyancy force is also called Archimedes force or lift force.
Forces acting on a solid immersed in a fluid substance
It is important to know these forces in order to answer the question whether the body will swim or sink. In general, there are only two of them:
- gravity or body weight F g ;
- buoyancy force F A.
If F g > F A , then it is safe to say that the body will sink. On the contrary, if F g <F A , then the body will stay on the surface of the substance. To sink it, it is necessary to apply an external force F A -F g .
Substituting the formulas for the indicated forces into the indicated inequalities, we can obtain the mathematical condition for swimming bodies. It looks like this:
Ο s <Ο l .
Here Ο s is the average density of the body.
It is not difficult to demonstrate the operation of the above conditions in practice. It is enough to take two metal cubes, one of which is solid, and the other is hollow. If you throw them into the water, the first will drown, and the second will float on the surface of the water.
The use of buoyancy in practice
All vehicles that move on or under water use the Archimedes principle. So, the displacement of ships is calculated on the basis of knowledge of the maximum buoyancy force. Submarines, changing their average density with the help of special ballast chambers, can float or dive.
A striking example of a change in average body density is the use of life jackets by a person. They significantly increase the total volume and at the same time practically do not change the weight of a person.
The rise of a balloon or helium balloons inflated by helium in the sky is a vivid example of the action of buoyant Archimedean force. Its appearance is due to the difference between the density of hot air or gas and cold air.
The task of calculating the Archimedean force in water
A hollow ball is completely submerged in water. The radius of the ball is 10 cm. It is necessary to calculate the buoyancy force of water.
To solve this problem, you do not need to know what material the ball is made of. It is only necessary to find its volume. The latter is calculated by the formula:
V = 4/3 * pi * r 3 .
Then the expression for determining the Archimedean force of water is written in the form:
F A = 4/3 * pi * r 3 * Ο l * g.
We substitute the radius of the ball and the density of water (1000 kg / m 3 ), we find that the buoyancy force is 41.1 N.
The task of comparing Archimedean forces
There are two bodies. The volume of the first is 200 cm 3 , and the second is 170 cm 3 . The first body was immersed in pure ethyl alcohol, and the second in water. It is necessary to determine whether the buoyant forces acting on these bodies are the same.
The corresponding Archimedean forces depend on the volume of the body and on the density of the liquid. For water, the density is 1000 kg / m 3 , for ethyl alcohol - 789 kg / m 3 . We calculate the buoyancy force in each fluid using these data:
for water: F A = 1000 * 170 * 10 -6 * 9.81 β 1.67 N;
for alcohol: F A = 789 * 200 * 10 -6 * 9.81 β 1.55 N.
Thus, the Archimedean force in water is 0.12 N greater than in alcohol.