  Obtaining pressure field data from particle image velocimetry (PIV) is an
attractive technique in fluid dynamics due to its noninvasive nature. The
application of this technique generally involves integrating the pressure
gradient or solving the pressure Poisson equation using a velocity field
measured with PIV. However, very little research has been done to investigate
the dynamics of error propagation from PIV-based velocity measurements to the
pressure field calculation. Rather than measure the error through experiment,
we investigate the dynamics of the error propagation by examining the Poisson
equation directly. We analytically quantify the error bound in the pressure
field, and are able to illustrate the mathematical roots of why and how the
Poisson equation based pressure calculation propagates error from the PIV data.
The results show that the error depends on the shape and type of boundary
conditions, the dimensions of the flow domain, and the flow type.
