A novel method is introduced to estimate phase-averaged pressure and acceleration of the coherent structures. It is applied and validated in the near wake of a two-dimensional bluff body. The method is validated using synthetic data generated by simulating an unsteady laminar flow around a D-shaped bluff body; the effect of noise is investigated to simulate an experimental scenario. The acceleration terms, required for the closure of flow-governing equations, are accurately estimated using this approach. The findings demonstrate that the methodology outputs consistent results for the pressure field while combined with a divergence-correction scheme, based on Helmholtz decomposition, and an optimal control method using sparse sensor measurements. The approach is later validated on experimental data obtained in the turbulent wake of a bluff body by means of “Particle Image Velocimetry” (PIV). Triple-decomposed flow fields are provided as input, where triple-decomposition refers to the instantaneous flow fields split into a mean flow, coherent and incoherent structures. The coherent structures are extracted using the method of “Proper Orthogonal Decomposition” (POD). Coherent lift coefficients, estimated using integral budgets of momentum, remain within the sensor-measured range, whereas coherent drag coefficients show excellent agreement. Moreover, a significant reduction in the residuals, arising from the balance of the flow-governing equations, is achieved. Although the temporal information is lost when computing POD modes, the proposed method is able to recover it and estimate the pressure. Accordingly, the method can be extended to any time-dependant modal decomposition, thereby providing a low-cost alternative to expensive “time-resolved” PIV (tr-PIV) measurements.