In tokamak experiments, sufficiently strong E × B flow shear reduces turbulent transport, thereby improving the prospects for fusion power plants. It is therefore of great importance to efficiently explore parameter space to find where strong plasma flow can be achieved. To this end, we propose a new, physically motivated quasi-linear model for estimating momentum transport from turbulence in the presence of toroidal flow shear and plasma shaping. The method gives good estimates of momentum transport for up–down asymmetric geometries as well as low magnetic shear and tight aspect ratio. The results are benchmarked with high-fidelity nonlinear GENE simulations, demonstrating that it provides a fast and accurate estimate of momentum transport.