DETERMINATION OF THE COMPRESSED FLOW DEPTH IN THE BRIDGEHEAD OF A SMALL BRIDGE

Abstract

Introduction. Hydraulic calculation of bridges is one of the most important stages in determining its basic geometric parameters. Therefore, it should be based on the exact equations of hydraulics that characterize the behavior of water flow. Currently, the hydraulic calculation of a small bridge is based on an empirically established dependence, which is that the compressed depth under the bridge hc is associated with the support H approximate dependence hc ≈ 0,5H and is independent of the compression of the flow bridge crossing. In this work, it is theoretically proved that taking such a relationship between depths, you can get quite large inaccuracies in determining the depth in the compressed section hc, and hence in determining the speed in the calculated cross section of the bridgehead. Results. Based on the three basic laws of physics, namely: the law of conservation of mass (continuity equation), the law of conservation of energy (Bernoulli equation), the law of momentum (equation of the momentum change theorem), obtained an analytical relationship that establishes a relationship between compressed depth parameters hc and support H at different degrees of flow compression ε. Based on this dependence, an equation was obtained that establishes the relationship between the flow rate Q and the pressure in front of the bridge H. The obtained equation is similar in form to the flow equation through a wide-threshold spillway, with the difference that the flow coefficient m(ε) in the obtained equation depends on the degree of flow compression. Conclusions. The equation for determining the flow rate through the opening of a small bridge taking into account the flow compression is obtained. It is shown that the obtained equation coincides in form with the flow equation, which determines the flow through a wide-threshold spillway. The difference between these equations is that the flow coefficient m(ε) is a function of the flow compression coefficient ε. Using the boundary transition, it is obtained that m(ε) can vary from 1/3 √(2/3) to √0,5. Graphs are presented, which allow to analyze the change of hydraulic characteristics of the flow depending on the compression coefficient ε.