If the speed of a fluid increases, then its static pressure or potential energy must decrease in compensation.

For an ideal fluid, the sum of kinetic, potential, and pressure head remains constant.

What this means, is that either a fluid moves due to potential energy(from a point of elevation, for example) or due to a difference pressure.$^5$

However, the most important point from this principle is that a fast-flowing fluid has a lower pressure.$^5$

When you say kinetic or potential or pressure head, you mean the kinetic or potential or pressure by the volume of the fluid. However this is not necessary to learn at this level.

Ideal Fluid

An ideal fluid is one that is non-viscus(no friction), incompressible(density is constant), streamlined(no turbulence).

Equation

The equation quantifies the principle.

$$ P + \frac12\rho v^2 + \rho gh = \text{const} $$

$P$ is the pressure, $\rho$ is the density of the fluid, $v$ is the fluid speed(not velocity), $g$ is acceleration due to gravity, and $h$ is the height or depth. The first term is pressure, the second term is the kinetic energy of the fluid per unit volume, the third term is the gravitation potential energy per unit volume for the fluid.$^5$

Application

In order to apply the equation, you use the following:

$$ P_1 + \frac12\rho v_1^2 + \rho gh_1 = P_2 + \frac12\rho v_2^2 + \rho gh_2 $$

You can use this for nonuniform cross-sectional objects.

For a horizontal tube, $h_1$ and $h_2$ are equal. Hence $\rho gh$ cancels. The equation becomes:

$$ P_1 + \frac12\rho v_1^2 = P_2 + \frac12\rho v_2^2 $$

$P$ and $v^2$ are inversely proportional to each other.

Continuity Equation

The product of the area of the cross section and speed of the airflow remains constant.