  A recent study investigated the propagation of error in a Velocimetry-based
Pressure (V-Pressure) field reconstruction problem by directly analyzing the
properties of the pressure Poisson equation (Pan et al., 2016). In the present
work, we extend these results by quantifying the effect of the error profile in
the data field (shape/structure of the error in space) on the resultant error
in the reconstructed pressure field. We first calculate the mode of the error
in the data that maximizes error in the pressure field, which is the most
dangerous error (called the worst error in the present work). This calculation
of the worst error is equivalent to finding the principle mode of, for example,
an Euler-Bernoulli beam problem in one-dimension and the Kirchhoff-Love plate
in two-dimensions, thus connecting the V-Pressure problem from experimental
fluid mechanics to buckling elastic bodies from elastic mechanics. Taking
advantage of this analogy, we then analyze how the error profile (e.g., spatial
frequency of the error and the location of the most concentrated error) in the
data field coupled with fundamental features of the flow domain (i.e., size,
shape, and dimension of the domain, and the configuration of boundary
conditions) significantly affects the error propagation from data to the
reconstructed pressure. Our analytical results lend to practical applications
in two ways. First, minimization of error propagation can be achieved by
avoiding low-frequency error profiles in data similar to the worst case
scenarios and error concentrated at sensitive locations. Second, small amounts
of the error in the data, if the error profile is similar to the worst error
case, can cause significant error in the reconstructed pressure field; such a
synthetic error can be used to benchmark V-Pressure algorithms.
