Effect of shear rate and proximity of a wall
The presence of a velocity gradient in a boundary layer does not involve a gradient of static pressure but the gradient of stagnation pressure produces a deviation of streamlines towards the lowest speed and then induces variations in the pressure read by the probe. A similar phenomenon occurs for the downwash on the support of the probe. The proximity of a wall increases the speed and decreases the pressure on one side of the probe; errors less than 1% in detecting the static pressure are made only if the probe is kept at a distance of at least 5 diameters from the wall.
Both phenomena actually discourage the use of static probes for measurements in the boundary layer: since static pressure is constant in the layer, it can be measured in a hole in the wall.