To describe the behavior of fluids in different situations, it is important to know the basic principles.

## Basic Principle of Hydrostatic (Stevin's Principle)

The difference between the pressures of two different points within a liquid in equilibrium is proportional to the density of the liquid, $$\rho$$, the gravity acceleration module, $$g$$, and the differences in the heights of the points considered $$h$$. Mathematically, we have $$\Delta P = P_B - P_A = \rho g h.$$

The distribution of pressure in a fluid is due to:
1. the existence of a gravitational field
2. an acceleration of the fluid by external forces (non-gravitational)
3. a combination of both causes.

Importantly, for the air, as the density is very low, we can ignore the pressure variation with height when this variation is of the order of a few meters.

### Consequences of Stevin's Principle

1. Points that support the same pressure belong to a same horizontal plane. Effect: The whole free surface of a liquid in equilibrium is horizontal.
2. When immiscible liquids (those which do not mix) are placed in a container, they are disposed from the bottom to the top of the container, in descending order of their densities. The separation surface between two non-miscible liquids is flat and horizontal.
3. If two immiscible liquids are placed in a U-shaped tube, the heights reached by the liquids, from the separation surface, are inversely proportional to the specific masses of the liquids, i.e., $$\frac{h1}{h2} = \frac{\rho_2}{\rho_1}.$$

### Pascal's Law

A pressure variation occurring at any point in an equilibrium liquid is transmitted integrally to all points of the liquid.

That is, for a smaller area $$a$$ in relation to a bigger area $$A$$ in a fluid, a lower intensity force $$f$$ can balance a stronger force $$F$$, depending on the ratio $$\frac{a}{A}$$.

This principle is used in workshops, in the machines that suspend the cars and also in the brakes and directions of some vehicles.