The main contribution of the paper is to incorporate pipe-wall viscoelastic and unsteady friction in the derivation of the water-hammer solutions of non-conservative hyperbolic systems with conserved quantities as variables. The system is solved using the Godunov finite volume scheme to obtain numerical solutions. This results in the appearance of a new term in the mass conservation equation of the classical governing system. This new numerical algorithm implements the Godunov approach to one-dimensional hyperbolic systems of conservation laws on a finite volume stencil. The viscoelastic pipe-wall response in the mass conservation part of the source term has been modeled using generalized Kelvin–Voigt theory. For the momentum part of the source term a fast, robust and accurate numerical scheme linked to the Lambert W-function for calculating the friction factor has been used. A case study has been used to illustrate the influence of the various formulations; a comparison between the classical solution, the numerical solution including quasi-steady friction, the numerical solution incorporating the viscoelastic effects, and measurements are presented. The inclusion of viscoelastic effects results in better agreement between the measured and solved values.
In the event of an instantaneous valve closure, the pressure transmitted to a surge tank induces the mass fluctuations that can cause high amplitude of water-level fluctuation in the surge tank for a reasonable cross-sectional area. The height of the surge tank is then designed using this high water level mark generated by the completely closed penstock valve. Using a conical surge tank with a non-constant cross-sectional area can resolve the problems of space and height. When addressing issues in designing open surge tanks, key parameters are usually calculated by using complex equations, which may become cumbersome when multiple iterations are required. A more effective alternative in obtaining these values is the use of simple charts. Firstly, this paper presents and describes the equations used to design open conical surge tanks. Secondly, it introduces user-friendly charts that can be used in the design of cylindrical and conical open surge tanks. The contribution can be a benefit for practicing engineers in this field. A case study is also presented to illustrate the use of these design charts. The case study's results show that key parameters obtained via successive approximation method required 26 iterations or complex calculations, whereas these values can be obtained by simple reading of the proposed chart. The use of charts to help surge tanks designing, in the case of preliminary designs, can save time and increase design efficiency, while reducing calculation errors.
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