آزمون كاربردي فرمول هاي متداول طراحي زهكش ها بر اساس شرايط واقعي جريان متغير مكاني با سطح آزاد

Application Assessment of the Conventional Drain Diameter Design Formula Based on Actual Free Surface Spatially Varied Flow Conditions

In this research, the governing equation of the spatially varied flow for a circular pipe was derived and its applicability in determining the flow conditions and the drain pipe diameter computation was evaluated. Also, the discreate forms of the governing equations were solved numerically using the Newton-Raphson method. The assumptions accepted in deriving the traditional equations eliminated the pipe length from the formulation, while this parameter affects the spatially varied flow solution. Therefore, it was necessary to establish a criterion, which makes the comparison between the result of the traditional equations and that of the spatially varied flow method possible. It was assumed that a discharge, which forces the water surface profile to reach the pipe crown at upstream end is comparable to that of the traditional equation. Numerical results of discharge-diameter relationship for different pipe lengths and longitudinal slopes indicated that for the practical slope range, i.e. 0.001 to 0.005, the results of the SVF approximately correspond to the non-uniform flow equation results for the lower limit slopes within the range. But they proceed towards the uniform flow equation results as the slope increases. However, this correspondence or even the concordance does not reflect identical results, since the flow condition in the SVF along the conduit is free surface one, while the traditional equations assume a pipe running full and having hydraulic grade line which concords with the pipe crown or sits a slightly higher than the top of the pipe. In other words, if any cross section rather than the upstream end one was considered full in the determination of the discharge-diameter relationship based on the spatially varied flow method, different results would be expected. That is, smaller diameters would be determined to convey the same discharge values. Therefore, the results of the non-uniform formula, although still conservative, are more realistic compared to the results of the uniform flow formula. This is because of the inherent safety factor in the diameter computation. A diameter determined based on the non-uniform formula would even bear some pipe obstruction (such as sedimentation) without drastically reducing the conveyance capacity of the pipe.