A flame speed expression proposed recently is studied in detail and extensively validated in this study. This expression has no adjustable parameters, and its constants are closely tied to the physics of scalar mixing at small scales. In the weak turbulence limit, the flame speed expression recovers a linear dependence of the turbulent to laminar flame speed ratio, S-T/S-L(o), on the normalized turbulence rms velocity, u'/S-L(o), in accordance with Damkohler's classical result. However, in the limit of intense turbulence, Damkohler's result gives a square-root dependence, while the new expression gives a combination of linear and square-root terms. Predictions of the new expression are compared to a wide range of experimental data of S-T from various flame configurations and conditions, with the same values of the model constants. The quantitative comparisons are found to be very good with experimental data beyond the usually restricted range of u'=S-L(o) of existing models. Predictions of S-T for high-pressure turbulent flames, up to 3 MPa, also compare acceptably well with experimental measurements. The flame speed is found to increase when the mean curvature of the flame brush is positive, and this dependence seems to be linear.