what is pascal's law state and prove it

Pascal's Law, named after the French scientist Blaise Pascal, states that when a change in pressure is applied to an enclosed fluid, it is transmitted undiminished to all portions of the fluid and to the walls of its container. This principle is fundamental to the operation of hydraulic systems.

Here's a step-by-step proof of Pascal's Law:

1. Consider a fluid enclosed in a container. The fluid is in equilibrium, meaning there are no net forces acting on it.

2. Now, apply an external pressure to a small area of the fluid. This can be done by pushing a piston into the container, for example.

3. According to the definition of pressure (force divided by area), the force exerted by the piston is distributed over the entire area of the piston. This force causes a change in pressure in the fluid.

4. Because the fluid is incompressible, it cannot absorb this change in pressure. Instead, the change in pressure is transmitted throughout the fluid.

5. The change in pressure is the same at all points in the fluid, because the fluid is in equilibrium. This means that the pressure at any point in the fluid is the same in all directions.

6. Therefore, the change in pressure applied to the fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. This is Pascal's Law.

This principle can be observed in many real-world applications, such as hydraulic brakes and hydraulic lifts, where a small force applied to a small area can create a large force over a large area.