Improved Analytical Solution for Water Hammer in Viscoelastic Pipes

Document Type : Research Studies

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Houston, Irrigation & Hydraulics Department, Faculty of Engineering, Mansoura University, El-Mansoura 35516, Egypt.

Abstract

The challenge of the present paper is improving an analytical solution for the one-dimensional water hammer in viscoelastic pipeline due to sudden end valve closure. The importance of the analytical solution is providing the necessary design information, especially in absence of an analyzing software. New exact dimensionless analytical equation is derived to determine the attenuated pressure wave head along the first pressure wave trip, and the viscoelastic term is merged in the wave celerity expression. Then, the integration process is utilized to rederive an approximate analytical equation for the pressure head at the valve during the first half pressure wave cycle, which involves the maximum design pressure head. Performance of the analytical results is compared with numerical results of the method of characteristics, for nearly all literature studies of the problem. Perfect performance for the analytical results is obtained for frictionless pipes that are a little bit distorted as the ratio, of the steady state friction head losses in the pipe to the Joukowsky pressure head, increases. Therefore, a nonlinear deterministic optimization algorithm is adopted to improve the integration constant of the friction term, which enhances the accuracy of the analytical results.

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