Examination of the physical assumptions of a quasi-steady vector model using the integral momentum equation

Quasi-Steady (QS) vector models have served as a convenient and effective tool for wind load estimations for low-rise buildings in the wind engineering community. In order to understand the applicability for practice, the physical assumptions of a QS vector model are investigated in this paper. The derivation is done through algebraic manipulation of the time-averaged integral momentum equation, which is used to relate mean, area-averaged, roof surface pressures to the mean flow and turbulence field above a roof. The two main assumptions of the QS model are revealed through this process: (i) The streamlines of an instantaneous flow near the roof are assumed to be the mean streamlines so that the instantaneous direction of the flow measured at the reference point is equivalent to the mean direction; (ii) The magnitude of the instantaneous flow is obtained by amplifying the magnitude of the mean flow at a spatially uniform rate such that the amplified magnitude of mean velocity is equivalent to the instantaneous magnitude measured at the reference point. Missing terms in the QS model are used to develop correction terms to improve QS model performance.