The effect of velocity filtering in pressure estimation

Velocity field measurements allow, in principle, the evaluation of the pressure field by integrating the equations of fluid motion. Unavoidable experimental uncertainty, however, may result in unreliable estimates. In this study, we use the Poisson pressure equation to estimate the relative pressure from experimental velocities, and investigate how pre-processing with smoothing and solenoidal filters affects this estimate. For diffusion dominated laminar flow or for turbulent flow modeled through an eddy viscosity, measurement noise significantly affects the results. In this case, solenoidal filtering provides superior performance over other smoothing approaches, as it preserves the second spatial derivatives of the velocity field. For laminar flows dominated by advection or acceleration components of the pressure gradient, the choice of the filter appears to have little effect under limited noise, while smoothing produces improved relative pressure estimates for higher noise intensities. The above statements are verified using idealized flow conditions, numerical fluid dynamics simulations, and velocity fields from in-vivo and in-vitro magnetic resonance velocimetry.