For a steady, incompressible flow with negligible viscous dissipation, mechanical energy along a streamline can be written as

$$p+\frac12\rho v^2+\rho gh=\text{constant}.$$

This is Bernoulli's equation.

Three contributions

The pressure term $p$ represents pressure energy per unit volume, $\tfrac12\rho v^2$ the kinetic contribution and $\rho gh$ the gravitational potential contribution.

If elevation is unchanged, increasing velocity along a streamline is accompanied by decreasing static pressure when the assumptions of the equation hold.

Using continuity with Bernoulli

In an incompressible pipe flow,

$$A_1v_1=A_2v_2.$$

A restriction can therefore increase velocity, after which Bernoulli's equation relates that change to pressure.

Limits of the model

Bernoulli's equation in this form neglects viscous energy loss and assumes steady incompressible flow. Pumps, turbines and significant friction require additional energy terms or a more complete momentum/energy model.