This whole subject is related to the principle of conservation of energy. If we assume that no energy is added to or removed from our air stream, then the total energy must remain constant.
If we look at a moving mass of air we can see that it's total energy is the sum of the following parts.
1. Mechanical energy due to its static pressure. (this is the energy that permits compressed gasses to carry out work when they expand, as for example in a piston engine).
2. Kinetic energy due to its velocity (this is evident in the form of the dynamic pressure).
3. Potential energy by virtue of its height above some reference point.
4. Thermal energy (this is evident by virtue of its temperature).
If we simplify our experiment by assuming that the flow is horizontal, then the potential energy will be constant.
If we now introduce our air stream into a tube at some selected velocity, its total pressure energy will be the sum of the static pressure plus the dynamic pressure.
If the tube becomes narrower, the velocity must increase to permit the flow to continue at the same mass flow rate. This will increase the dynamic pressure.
But(if we ignore friction) the narrowing of the tube will not introduce or remove any energy, so the total pressure energy must remain constant. This means that the static pressure must decrease to offset the increasing dynamic pressure. The above scenario is an example of a situation in which the total pressure remains constant.
Now let's look at what happens when an aeroplane accelerates during the take-off run. Its engines provide a great deal of energy to accelerate it up to flight speed. This increases the dynamic pressure. But this increase in dynamic pressure is being funded by the engines, so there is no compensating reduction in static pressure. The overall result is that as the aircraft accelerates, the total pressure of the air flowing over its surfaces increases.
But if we look closely at its curved surfaces we can still see that localized trade-offs between static pressure and dynamic pressure are taking place. As the air flows over the nose for example, the curved surfaces cause the local airspeed to increase. This increases the local dynamic pressure and decreases the local static pressure. But these local changes are being applied to a total pressure which is already much higher than the ambient value.