Study On The Equations Of Hydraulic Jump In Stilling Basin With Upstream Expansive Slope

Stilling basin with upstream expansive slope is well adapted to project demands, itsdiffusion body and hydraulic jump make the energy dissipation effect well and be adapted towater level changes in downstream. The energy dissipation effect of stilling basin withupstream expansive slope is good, it can protect the downstream slope and shorten the lengthof stilling basin. In the practical project, stilling basin with upstream expansive slope has arelatively wide range of applications, such as hydropower station of Bulunkou, hydropowerstation of XIHE, etc. However, there are less researches about the hydraulic jump formula ofstilling basin with upstream expansive slope. Therefore, according to the practical demands,conducting on hydraulic characteristics of stilling basin with upstream expansive slope deeplyand seeking more simple and accurate formula of hydraulic jump have important significancein designing energy dissipation and erosion of downstream dam. For the problem of lessresearch about the hydraulic jump formula of stilling basin with upstream expansive slope, thefollowing studies were conducted in this paper:（1） Based on statistics of model experiment data about the hydraulic jump, therelational expression between the water depth ratio and the Froude numbers was obtained oncontrast to experimental data, the result of analysis has little error. The relative standard errorsare1.07%、1.14%、0.23%、2.64%、4.08%、0.00%. The average relative error is lower than5%. These new formulae, with simple form and good accuracy, are easy to be applied inengineering practice. The study illustrated that the method is capable to meet the demands ofproject application. The method provides a new explication for study in stilling basin withupstream expanding slop.（2）In the specific type of stilling basin which studied in this paper, the hydraulic jumplength was related to the Froude numbers and water depth ratio. That was inconsistent withpresent study conclusion of hydraulic jump accrued in normal flat rectangular stilling basin.The hydraulic jump length is proportionate to the Froude numbers and water depth ratio. Arelationship exists between the dissipation ratio of the hydraulic jump and the Froudenumbers. The dissipation ratio of the stilling basin is proportionate to the Froude numbers infront section of hydraulic jump. As the increase of the Froude numbers, the increase of dissipation ratio reduces.（3）The calculation problem about weight force of hydraulic jump in stilling basin withupstream expansive slope was solved using integral approach and the theoretical formula wasdeduced through the combination with momentum equation and continuity equation. Thecurrent various calculation methods were analyzed by using experimental data, then differentcalculation results were compared. Various calculation methods include U.S. Army Corps ofEngineers algorithm, Zhou Ming Tak algorithm, Li Qiong algorithms and theoretical formulaof water jump deduced in this article. The relative standard errors are2.73%、1.38%、0.28%、3.06%、3.55%,The average relative error is1.87%. The results have shown that the newmethod results were in accordance with the experimental. The new method is accurate andreliable. It also can provide a reference for piles analysis and design.（4）The theoretical formula is analyzed through changing the body condition. Thenapplication of formula in fold slope hydraulic jump and flat rectangular hydraulic jump wereanalyzed. Results showed that the formula can be used in fold slope hydraulic jump afterdeformation. Theoretical formula is consistent with the existing conjugate depth calculationformula of flat rectangular hydraulic jump.