Comparison of calculation results on a hydraulic slope in gravity drainage networks using classical and refined A. Chézy formula

In the present work, we compare the calculation results by the classical Antoine Chézy formula and refined Prodous - Shlychkov formula. Unlike the classical formula for the hydraulic calculation of gravity drainage networks introduced in 1769, the new formula includes the thickness of an actual deposit layer in pipe water troughs. Using the A. Chézy formula for the hydraulic calculation of new pipes made of different materials provides sufficient practical accuracy; however, no studies have been performed for pipes with deposits in the water troughs. The Chézy formula is characterized by the denominator having the reduced pipe diameter, which takes into account the effect of the thickness h associated with a sediment layer. To compare the precision of the two formulas, a practical problem should be solved. For that, a specific example is necessary to compare the calculation results  of  hydraulic  slope  i,  obtained  using  the  classical  Chézy  formula  and  refined  Prodous - Shlychkov formula. Analysis of the values of pipe characteristics indicates that the presence of a deposit layer h = 0.1 m in the water troughs leads to an increase in the gravity flow rate from V_n = 0.88 m/s to V_pr = 2.0 m/s (2.27 times) and the hydraulic slope from i_n = 0.00282 m/m to i_pr = 0.02527 m/m (8.96 times). Therefore, introducing the dpr  value to the formula allows more accurate results in the hydraulic calculation of the hydraulic slope i_pr  to be obtained for pipes with deposits in their water troughs. An example of hydraulic calculation for pipes with deposits and the dependency graph of the hydraulic slope as a function of the actual flow rate are provided. The obtained values are summarised in a table with pipe characteristics depending on different gravity flow rates. It is recommended to introduce the refined A. Chézy formula to the normative standard RR 32.13330.2012.

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