  An analytical framework for the propagation of velocity errors into PIV-based
pressure calculation is extended. Based on this framework, the optimal spatial
resolution and the corresponding minimum field-wide error level in the
calculated pressure field are determined. This minimum error can be viewed as
the smallest resolvable pressure. We find that the optimal spatial resolution
is a function of the flow features (patterns and length scales), fundamental
properties of the flow domain (e.g., geometry of the flow domain and the type
of the boundary conditions), in addition to the error in the PIV experiments,
and the choice of numerical methods. Making a general statement about pressure
sensitivity is difficult. The minimum resolvable pressure depends on competing
effects from the experimental error due to PIV and the truncation error from
the numerical solver, which is affected by the formulation of the solver. This
means that PIV experiments motivated by pressure measurements should be
carefully designed so that the optimal resolution (or close to the optimal
resolution) is used. Flows ($Re = 1.27 \times 10^4$ and $5\times 10^4$) with
exact solutions are used as examples to validate the theoretical predictions of
the optimal spatial resolutions and pressure sensitivity. The numerical
experimental results agree well with the rigorous analytical predictions. We
also propose an \textit{a posterior} method to estimate the contribution of
truncation error using Richardson extrapolation and that of PIV error by adding
artificially overwhelming noise. We also provide an introductory analysis of
the effects of interrogation window overlap in PIV in the context of the
pressure calculation.
