Why is the pressure of the liquid equal in all directions at the same depth inside the liquid?

The problem is actually quite complex, and rigorous proofs require the use of some advanced mathematical tools such as tensors. I can only talk about it briefly.

The conclusion that the pressure inside the liquid is equal in all directions at the same depth is only true in Newtonian fluids. What is Newtonian fluid, that is, there is only positive pressure between the inside of the liquid, and there is no tangential force. That is, the liquid has no viscosity, and the liquid in the upper half does not exert a force in the horizontal direction on the lower half of the liquid, and similarly, the liquid on the left does not exert a vertical force on the liquid on the right.

This is a basic assumption. In fact, there is no such thing as a true Newtonian fluid in nature, but a less viscous liquid such as water can be considered a Newtonian fluid.

Under the basic assumption of Newtonian fluids, I take a microelement inside the liquid, and what forces are applied to this microelement, which is naturally subjected to positive pressure in six directions, but not in the tangential direction. Since the liquid is a stationary liquid, the pressure in the horizontal direction should be balanced with each other, and the pressure in the vertical direction should be balanced with the gravity of the microelement.

Not only that, but there is a condition for these forces, such as a force in the horizontal direction, where two mutually balanced forces will cause the microelement of water to stretch in the other direction, because it is not balanced by a tangential force. So there must be another pair of equilibrium forces in the direction of tension. According to the isotropy of water, these two pairs of equilibrium forces must be equal, otherwise either the equilibrium condition is not satisfied, or the water is anisotropic.

The same goes for the vertical direction.

Integrating such an equilibrium equation can also lead to the conclusion that the magnitude of the pressure is f= gh, so this pressure formula is also valid under the condition of Newtonian fluid.

Think about your belt :) tighten up, huh.

There is shear stress in the actual fluid movement, so the magnitude of the compressive stress (i.e., pressure) is related to the orientation of the action surface, and the pressure in the three mutually perpendicular directions is generally unequal, that is, px, py, and pz are not equal. But in theoretical fluid mechanics, it can be proved that the average value p of the pressure in the three orthogonal directions at the same point is a single value, which is independent of the bearing.

In practical terms, the average value (px+py+pz) 3 is used

As the pressure p at the point, the pressure of the actual fluid is also only a function of the position coordinates and time, i.e.

p=f(x,y,z,t), in a constant flow p=f(x,y,z,). The pressure in the three directions at the same point can be expressed as.

px=p+px’，py=p+py’,pz=p+pz’。px', py', pz' are additional pressures in the three directions, respectively, and these additional pressures are the corresponding results due to viscosity. Additional pressure and viscosity of the fluid

It is related to the linear deformation velocity: px'=-2 (δux δx)py'=-2 (δuy δy)pz'=-2 (δuz δx).

Because the liquid is subject to gravity and is fluid, the liquid has pressure on the bottom of the container and the side walls of the container, and the inside of the liquid is pressurized in all directions.

1. In liquid.

Imagine an object (above).

2. Analyze the liquid from all directions in the extrusion of the object (this genus can show that the liquid pressure is in all directions).

3. Constantly remove the height of the object (H1 increases, H2 decreases), then P increases downwards and P decreases upwards. When h2=h1=hleft=hright, p down=pup=pleft=pright(this can illustrate the same depth, up, down, left, and right pressure is equal).

It's a bit hard for you to understand that way.

Switch angles. Because the pressure of the liquid is small, it is related to the depth of the liquid, the density of the liquid.

And the same depth, liquid depth, and liquid density are all the same in the liquid, so the pressure is the same.

Pressure has no direction, it is only related to depth, and it is pressure that has direction.

In addition, the pressure is actually the opposite of the elastic deformation effect.

Exclusive screening, which has nothing to do with gravity.

(or gravity is an indirect cause). At the same point, the liquid pressure is the mutual extrusion inside the liquid, that is, the relationship between the action force and the reaction force, so the magnitude is equal.

There's gravity and there's buoyancy.

The use of U-shaped tube piezometer** The pressure of the same liquid at the same depth in all directions is small and equal to the liquid pressure measuring instrument called "U-shaped tube piezometer", the liquid pressure formula p= hg, h is the depth of the liquid, and the pressure generated by calculating the liquid level difference is equal to the internal pressure of the liquid.

The liquid pressure is not easy to measure directly, and the conversion method used in this experiment is to compare the pressure generated by the liquid through the pressure gauge and the change of the liquid column of the U-shaped tube.

Steps: 1. Immerse the measuring head of the piezometer in the liquid, record the height of the liquid column 2, rotate the measuring head at the same depth, and observe whether the height of the liquid column changes the resultConclusion: The pressure of the same liquid at the same depth in all directions is the same.

Junior high school is not required and can be used directly.

High school can explain that microscopic speaking, liquid molecules move irregularly from time to time, and the constant movement involves gravitational force and the impact force of molecules, which is roughly the same force. Macroscopic theory means that the force is the same in all directions, and the pressure is equal.

The piezometer is placed at the same depth of the same liquid, so that the rubber film is oriented in different directions, and the liquid level difference on both sides of the U-shaped tube is observed to be the same.