# Classical Mechanics: Pressure of Liquids ### 1. The generation of liquid pressure

• Liquid due to the role of gravity, and thus the bottom of the container has pressure, and gravity has a close relationship with the show.
• Liquid because there is no fixed shape, can flow, and thus there is also pressure on the side walls of the container.
• Measurement of liquid pressure and principles.

①. Measurement: A liquid piezometer is used to measure the pressure inside a liquid.

②. Principle: When the rubber membrane on the probe is under pressure, the height difference between the two sides of the U-shaped tube, the height difference between the two sides indicates the size of the pressure, the greater the pressure, the greater the height difference between the liquid surfaces.

2、Characteristics of liquid pressure

A single variable comparison experiment is a common experimental method

1. liquid on the bottom and side walls of the container have pressure, liquid internal pressure in all directions.
2. the pressure of the liquid increases with the depth.
3. At the same depth, the pressure of the liquid is equal in all directions.
4. The pressure of different liquids is also related to the density of the liquid.

### 3. formula for calculating the pressure of a liquid

• The formula for calculating the pressure of a liquid: p = ρ liquid gh.
•  Using the formula for liquid pressure should pay attention to the problems

①. When using p = ρgh to calculate the pressure of a liquid, the unit of ρ should be kg/m3, the unit of h should be m, g = 9.8N/kg, and the calculated unit of pressure should be Pa.

②. The two concepts of depth and height are distinct: depth is the vertical distance from the free surface of the liquid to a point within the liquid, i.e. depth is measured from top to bottom; while height is the vertical distance from a point in the liquid to the bottom, i.e. height is measured from bottom to top. Correctly determining the magnitude of h is the key to calculating the pressure of a liquid.

③. The formula for liquid pressure, p = ρgh, shows that the pressure in the formula is the pressure of the liquid due to its own gravity; it does not include the applied pressure on the liquid. As g is a constant, so the pressure is only related to the density of the liquid ρ and depth h, and no relationship with the volume of the liquid and gravity, and the shape of the container is not relevant.

### 4.The pressure of the liquid on the flat bottomed container

The pressure inside the liquid is transmitted in all directions
As the liquid has mobility, stationary in the horizontal placement of the container of liquid, the pressure on the bottom of the container is not necessarily equal to the gravity of the liquid, only when the container is columnar, the pressure on the bottom of the container is equal to the gravity of the liquid. The bottom of the small mouth of the large container bottom pressure is less than the gravity of the liquid, the bottom of the large mouth of the small container bottom pressure is greater than the gravity of the liquid. The pressure of the liquid on the bottom of the container F = pS = ρghS, and the meaning of Sh is to the bottom of the container, the depth of the liquid for the volume of the column, that is, V column = Sh, so F = pS = ρghS = ρgV column = m column g = G column, the meaning of G column to V column for the volume of that part of the gravity of the liquid.

Conclusion: the horizontal placement of a flat-bottomed container with liquid by the pressure of the liquid (without regard to the atmospheric pressure on the surface of the liquid or the role of other forces on the surface of the liquid), its size is equal to the cross-sectional area of the bottom of the container, the height of the liquid depth of the column of gravity, and the shape of the container is not relevant.

### 5. Comparing the pressure of a solid with the pressure of a liquid

Pressure is an important concept in junior physics. Due to the different physical properties of solids and liquids, resulting in their pressure in the relevant laws are different, in the application of the very easy to confuse. The following examples are used to identify the differences:

1. solid pressure can only be generated in a certain direction; liquid due to mobility, the pressure generated in all directions have. 2. in equilibrium, the pressure added to the solid can only be transmitted along the direction of the force, constant size (such as hand pressure peg); added to the pressure on the closed liquid can be transferred in all directions of constant size (such as oil pressure jack).

3. In solving problems relating to the pressure of a solid, if specific conditions are satisfied:

①. (i) the object is on a horizontal surface and the area under pressure is the base area of the object;

②. (ii) the volume of the object is equal to the base area multiplied by the height (e.g. a cylinder, rectangular body, etc.);

③. The solid should be a homogeneous object with a certain density. This also allows for the flexible use of the liquid pressure formula p = ρgh to find the pressure and simplify calculations.

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