Bernoulli equation and applications

What is the Bernoulli equation in fluid dynamics? Name two uses or practical applications of it.

Fluid-dynamics
Answer

The Bernoulli equation applies to non-compressible fluids, under steady state, and it says that the sum of the gravitational energy, pressure energy and kinetic energy will stay constant along the fluid path. That is:

$$P + \frac{\rho}{2} \cdot V^2 + \rho \cdot g \cdot h = cte$$

where: \(\begin{cases} P \quad [Pa] & \text{static pressure} \\ V \quad [m/s] & \text{fluid velocity} \\ h \quad [m] & \text{height} \\ g=9.81 \quad [m/s^2] & \text{gravity acceleration} \\ \rho \quad [kg/m^3] & \text{density of fluid}\end{cases}\)

It can be used to study what happens to the pressure along a pipe that moves in height. Some industrial applications are: Venturi meter, Pitot tube, Bunsen burner, deposit emptying equation...