Random Model And Solution To Surge And Waterhammer

The randomness of conditions under which waterhammer and surge occur and the factors that influence the magnitudes of watherhammer pressures and surge levels result in the stochasticism of waterhammer and surge. Based on a comprehensive study of the former research results, this dissertation makes a range of theoretical research on stochastic analysis of waterhammer and surge, and puts forward several conclusions that have been successfully verified by the results from computational examples, which agree completely with the results from the Monte-Carlo method.The dissertation reads as follows:1. The random model of waterhammer and surge and the distribution assumption of various random parameters are given on the basis of a summary of the existing research results both at home and abroad.2. The stochastic analysis of surge is made with pipe roughness and original load regarded as random variables. By use of the distributions of pipe roughness and original load, this dissertation draws the following conclusions: the formula for probability density function of hydraulic head-loss is rigidly deduced; the computational formula for probability density function of maximum value of relative surge level is rigidly deduced; the existence of the only mean square solution to the random model of surge is rigidly verified in mathematics; and the joint probability density function in solution processing of surge is solved with Liouville Equation.3."The stochastic analysis of waterhammer in a single system is made with water level of reservoir, original load, and valve closing regarded as random variables. By use of the valve closure linear relationship, the power series formula for the solution to the waterhammer pressure in a single system is derived. By use of the distributions of water level, original load and valve closure time, the integral formulas for probability density function of pressures of first interval type waterhammer and limit type waterhammer in a single hydraulic system are provided. The theoretical formulas for sensitivity analysis for waterhammer in a single system are given and, with these formulas, sensitivity analysis is made through examples. The method of distribution type fitting is introduced to determine the distribution of waterhammer pressures in single systems. Thereby conclusions are drawn that the distribution of increasing pressures of waterhammer in single systems is log-normal type and that of maximum pressures is normal type. By use of the distributions of water level, original load and valve closure time, moment characteristic method is presented for the solution to the mean value of waterhammer pressures in a single system.4. Computational examples are given to verify all the methods involved.