Open Channel Uniform Flow Velocity Distribution Law Research

Irrigation channels are usually wide depth ratio is less than 10 narrow deep channel, wall had a great influence on velocity of flow, but narrow deep type of open channel flow velocity distribution exists only some simple laminar flow velocity distribution in the cross section of the distribution of analytic solution, the turbulent velocity distribution at present there is no analytical solution. In view of the above problem, considering the influence of the lateral wall of open channel uniform flow velocity distribution, this article respectively to the engineering of commonly used standard uniform laminar flow velocity distribution of u-shaped channel and narrow deep type turbulent velocity distribution of rectangular open channel, the analytical solution of the theoretical derivation and numerical simulation, and further to its average velocity approximation formula calculated and test verification. The main results were as follows:(1) Standard of u-shaped channel complex cannot directly to solve poisson equations boundary, by assuming the u-shaped cross section of rectangle and semicircular joints velocity as parabolic distribution, decomposition region respectively to solve the rectangular area and semicircle region of velocity distribution, using the velocity function in the smooth continuity of joints, and the standard analytical solutions u-shaped channel laminar flow velocity distribution, and the numerical simulation is verified, velocity formula clear physical meaning, fully consider the influence of the boundary and the maximum error of 0.3%.(2) For narrow and deep channel turbulent flow velocity distribution, the selection of the most simple rectangular section to study, considering the narrow deep type rectangular channel wall effect on the velocity distribution, selected the parabola form to represent the lateral wall of the vertical velocity distribution, based on the three dimensional Reynolds equation, established the mathematical equation, conclude that the type of narrow rectangular channel wall influence the whole section of velocity distribution formula and the formula of transverse distribution of mean velocity, is verified with experiment, verification show that in the lateral wall of the measuring point error is around 6%, channel center area error within 3%; When the error is bigger, maximum error of 10%.(3) Of open channel uniform flow assumption the wall resistance and canal bottom resistance equal to, based on prandtl- Carmen rough flat two-dimensional open channel uniform flow velocity distribution formula of the trapezoidal channel, standards, u-shaped channel according to the length, equivalent to two dimensional open channel uniform flow, launched the trapezoidal channel, the standard of u-shaped channel section average flow velocity formula, and has made the comparison verification with the test results, the error is within 10%.The above formula, high precision, more clear physical meaning, can better reflect the velocity distribution characteristics, has high theoretical significance and practical value.