Watching the flight of balloons and the movement of ships on the sea surface, many people wonder: what makes these vehicles rise into the sky or keeps these vehicles on the surface of the water? The answer to this question is buoyancy. Let's take a closer look at it in the article.
Fluids and static pressure in them
Fluid are two aggregate states of matter: gas and liquid. The impact of any tangential force on them causes some layers of matter to shift relative to others, that is, matter begins to flow.
Liquids and gases consist of elementary particles (molecules, atoms), which do not have a definite position in space, as, for example, in solids. They are constantly moving in different directions. In gases, this chaotic movement is more intense than in liquids. Due to the noted fact, fluid substances can transmit the pressure exerted on them equally in all directions (Pascal's law).
Since all directions of movement in space are equal, the total pressure on any elementarythe 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 Earth's gravity field. 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 pressure. It increases in direct proportion to the depth h. So, in the case of a liquid with a density ρl, the hydrostatic pressure P is determined by the formula:
P=ρlgh.
Here g=9.81 m/s2- free fall acceleration near the surface of our planet.
Hydrostatic pressure has been felt by every person who has dived several meters underwater at least once.
Next, consider the issue of buoyancy on the example of liquids. Nevertheless, all the conclusions that will be given are also valid for gases.
Hydrostatic pressure and Archimedes' law
Let's set up the following simple experiment. Let's take a body of regular geometric shape, for example, a cube. Let the length of the side of the cube be a. Let us immerse this cube in water so that its upper face is at depth h. How much pressure does the water exert on the cube?
To answer the above question, it is necessary to consider the amount of hydrostatic pressure that acts on each face of the figure. Obviously, the total pressure acting on all side faces will be equal to zero (the pressure on the left side will be compensated by the pressure on the right). The hydrostatic pressure on the top face will be:
P1=ρlgh.
This pressure is downward. Its corresponding force is:
F1=P1S=ρlghS.
Where S is the area of a square face.
The force associated with hydrostatic pressure, which acts on the bottom face of the cube, will be equal to:
F2=ρlg(h+a)S.
F2force is directed upwards. Then the resulting force will also be directed upwards. Its meaning is:
F=F2- F1=ρlg(h+a)S - ρlghS=ρlgaS.
Note that the product of the edge length and the face area S of a cube is its volume V. This fact allows us to rewrite the formula as follows:
F=ρlgV.
This formula of the buoyancy force says that the value of F does not depend on the depth of the body's immersion. Since the volume of the body V coincides with the volume of the liquid Vl, which it displaced, we can write:
FA=ρlgVl.
The buoyancy force formula FA is commonly called the mathematical expression of Archimedes' law. It was first established by an ancient Greek philosopher in the 3rd century BC. It is customary to formulate Archimedes' law as follows: if a body is immersed in a fluid substance, then a vertically upward force acts on it, which is equal to the weight of the object being displaced by the body.substances. The buoyant force is also called the Archimedes force or the lifting force.
Forces acting on a solid body immersed in a fluid substance
It is important to know these forces in order to answer the question whether the body will float or sink. In general, there are only two of them:
- gravity or body weight Fg;
- buoyancy force FA.
If Fg>FA, then it is safe to say that the body will sink. On the contrary, if Fg<FA, then the body will stick to the surface of the substance. To sink it, you need to apply an external force FA-Fg.
Substituting the formulas for the named forces into the indicated inequalities, one can obtain a mathematical condition for the floating of bodies. It looks like this:
ρs<ρl.
Here ρs is the average density of the body.
It is easy to demonstrate the effect of the above condition 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 one will sink, and the second one will float on the surface of the water.
Using buoyancy in practice
All vehicles that move on or under water use the Archimedes principle. So, the displacement of ships is calculated based on the knowledge of the maximum buoyancy force. Submarines changingtheir average density with the help of special ballast chambers, can float or sink.
A vivid example of a change in the average density of the body is the use of life jackets by a person. They significantly increase the overall volume and at the same time practically do not change the weight of a person.
The rise of a balloon or helium-filled baby balloons in the sky is a prime example of the buoyant Archimedean force. Its appearance is due to the difference between the density of hot air or gas and cold air.
The problem of calculating the Archimedean force in water
The hollow ball is completely submerged in water. The radius of the ball is 10 cm. It is necessary to calculate the buoyancy of the 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=4/3pir3.
Then the expression for determining the Archimedean force of water will be written as:
FA=4/3pir3ρlg.
Substituting the radius of the ball and the density of water (1000 kg/m3), we get that the buoyancy force is 41.1 N.
Problem to compare Archimedean forces
There are two bodies. The volume of the first is 200 cm3, and the second is 170 cm3. 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/m3, for ethyl alcohol it is 789 kg/m3. Calculate the buoyancy force in each fluid using these data:
for water: FA=100017010-69, 81 ≈ 1, 67 N;
for alcohol: FA=78920010-69, 81 ≈ 1, 55 N.
Thus, in water, the Archimedean force is 0.12 N greater than in alcohol.
