Bernoulli's theorem

An increase of speed always occurs with a decrease in the pressure or the potential energy of a fluid.

Bernoulli's theorem is generally applied to incompressible fluids although it can also be applied to compressible liquids in more sophisticated forms.

Consider a liquid flowing in a tube.  If the area of the tube decreases in a certain section of the tube, the speed of the liquid in the section increases.  This is accompanied by a drop in the pressure of the liquid.

Bernoulli's theorem is based on the law of conservation of energy which states that the amount of energy in a flow that is steady is constant.  When the speed of the liquid increases, the kinetic energy increases.  To keep the total energy constant, there is a drop in the static pressure and the pressure energy.

Where P is the pressure energy
           ρ is the density
           v is the velocity and
           h is the head.