Analysis with Spatial Variations

The effect of spatial distribution of the measured variable over the probe on the frequency response is considered through two examples.

Example: Spatial variability in the probe response can cause additional attenuation in the output signal at the high frequency end. Consider a pitot tube of radius , length and subjected to a pressure gradient

The resulting flow at dynamic steady state is not only a function of time but also the radial coordinate since the velocity is zero at the tube walls and finite along its axis. Assuming a long tube and no edge effects, the Navier-Stokes equations can be reduced to