1. The concept of pressure and pressure

The pressure of liquid on the surface P=F/A is defined as the force acting on the area divided by the area, that is, p = f/a, where p refers to the pressure of liquid on the surface (Pascal), f refers to the force perpendicular to the surface, and a refers to the area of the surface.

2. The relationship between liquid depth and hydraulic pressure.

First of all, we can think that every tiny area in the liquid is subjected to the same pressure. The size of these tiny areas is dA and the depth is h, then the pressure of the liquid on dA can be expressed as dP = ρgdh, where ρ is the density of the liquid, g is the acceleration of gravity, and dh is the slight depth difference. For the whole liquid volume, the resultant force acting on the liquid can be expressed as F=∫PdA= ∫ρghdA, where the integral starts from the surface of the whole liquid to the end.

3. Mathematical deduction of liquid depth and hydraulic strength.

Divide both ends of this formula by a at the same time to get P=∫ρgdh, and the integral starts from the surface and ends at the depth h of the liquid. This definite integral is exactly the pressure p of the liquid, because the thickness of each layer of the liquid is dh and the pressure is ρgdh, and the pressure of each layer can be obtained by multiplying the top area of this layer. Therefore, the greater the depth of the liquid, the greater the pressure on each layer and the stronger the water pressure.

4. Practical application

Using this principle, people can calculate the depth of seawater, atmospheric pressure and so on. For example, the atmospheric pressure at sea level is about 10 1 325Pa, and it gradually decreases with the elevation.

5. Summary

In short, the liquid pressure is proportional to the depth, and the mathematical expression is P=ρgh. According to this principle, the pressure value of liquid at various depths can be calculated, and the problems in reality can also be reasonably explained.

6. Application scenarios

The relationship between liquid pressure and depth has many application scenarios in various fields. For example, when working underwater, it is necessary to calculate the pressure of liquids emitted at various depths on equipment and people to ensure the safe completion of the operation. The relationship between the pressure and depth of liquid, such as dams, reservoirs and water pipes, should also be considered in water conservancy projects.

In addition, in industrial production, liquid pressure control is also very important, because different production departments need different liquid pressures. According to the linear relationship between liquid depth and pressure, liquid pressure can be controlled by adjusting liquid level or liquid flow.