Study On The Basic Theory Of Water Hammer

In this thesis, the classic water hammer differential equation and mathematicmodels are introduced firstly. Some problems of the basic theory and numericalalgorithm are pointed. For example: the continuity equation of current water hammercomputation being used in the mathematical model can’t satisfy condition of steadyflow, the existence of sin is an unfairness question, the use of the momentumtheorem in the derivation of motion equation of water hammer computation is notreasonable, the confusion between ds/dt=v and ds/dt=ccand so on.In addition, based on the research of the basic differential equation of waterhammer, this paper would solve the above problems respectively: One dimensionalunsteady flow continuity equation is derived by three methods. The continuityequation of current water hammer computation being used in the mathematical modelcan’t satisfy condition of steady flow is due to the inappropriate introduction of wavevelocity of water hammer. Through the research, the introduction of wave velocity ofwater hammer is meaningless, except some physical meaning. Use the momentumtheorem to derive motion equation of water hammer strictly. The results consistentwith the classic water hammer motion equation. It illustrates that the original methoddon’t affect the results, although it’s not strict. This result shows that whether ignorethe wave velocity or not has no effect on the maximum pressure of water hammer. It’shelpful to the convergence result of the calculation of water hammer, but the result isnot consistent with actual situation. This illustrates ignoring wave velocity is not thecase reason of the fact that the calculation of water hammer don’t decay.Then, the new system of equations of water hammer calculation obtainedassociating with elasticity equation of conduit and elasticity equation of water byprecise deduction using new idea in this paper. The results of the variation rules aboutthe water head, the water hammer wave speed, the sectional area of the pipeline andthe liquid density considered reasonably. This thesis has importance in the theoreticalresearches and the water conservancy projects. Finally, by using the new system of equations of water hammer calculation, theclassification of the water hammer type and the influence of the valve opening factorson water hammer pressure are quantitative analyzed, and this paper get the influenceof the initial valve opening、the end of valve opening and the regular of valve openingfor water hammer pressure.