Bernoulli's Principle is used to describe the flow of fluids inside pipes of different pressures and different elevations; firstly, the fluid must be:

1. Incompressible: The fluid's density doesn't change with pressure
2. Non-Viscous: The fluid isn't thick and flows easily
3. Achieves Laminar Flow: The flow of the liquid isn't turbulent

A perfect example of a fluid that satisfies all three rules is: Water

Bernoulli's Principle is based on the Conservation of Energy, it states that the sum of energy (Kinetic + Potential + Internal) of a moving fluid at all points is constant, thus a change in the speed of a fluid's flow inside a container must be accompanied by a change in either the Pressure, or the Height: Where P is the pressure, raw is the fluid's density, v is the fluid's velocity, g is the gravitational potential, and h is the height / elevation of the tube.
Bernoulli's Equation states that:

Additionally, the area of the container plays a role in the change of the fluid's speed, the principle known as the Continuity Equation, which is based on the Conservation of Mass:

The Continuity Equation states that for an Incompressible, Non-Viscous, Fluid that is in Laminar Flow, The mass of fluid that moves in a certain time inside an area of the container is always constant: Where A is the area of the container, and v is the velocity of the fluid.
The Continuity Equation states that:

Applications of Bernoulli's Principle and the Continuity Equation Include: The Design of Aircraft Wings, and Pitot Tubes.