Modern analysis and control of unsteady flow in pipelines

This book is intended for the practising engineer who desires detailed instruction in the solution of water hammer problems of simple fluids in pipelines using a digital computer. The work is not a comprehensive treatise on unsteady flow, but concentrates primarily on water hammer problems and uses the method of characteristics exclusively to arrive at numerical solutions. The book takes the reader step by step through a series of examples of increasing complexity and provides a number of computer program listings. The material is presented in an organized fashion and at a level of sophistication normally reached with the Bachelor's degree. In the first chapter a very brief history of water hammer analysis is provided and the difference between rigid water column theory and elastic theory is explained. In the second chapter the phenomenon of surging is illustrated with examples and the unsteady flow equations are derived for flow of a simple fluid in a rigid circular pipe. This is followed in Chapt. 3 by examples of unsteady flow caused by valve closure (or opening) with the valve located at the end of a pipeline. This concludes the simple rigid water column theory. In Chapt. 4 the concept of water hammer is introduced in which an elastic fluid flows in an elastic pipe, resulting in two partial differential equations, the continuity and the Euler (including friction) equations. In Chapt. 5 the method of characteristics is introduced to solve the equations of Chapt. 4 numerically subject to various boundary conditions. A FORTRAN source program listing representing the behaviour of a pipeline connected to a reservoir and a valve (and a comparison of the program's predicted results with experimental data) completes this chapter. In Chapt. 6 the Hardy Cross, the linear theory, and the Newton-Raphson methods for solving steady state pipe network flow problems are introduced as a basis for the pipe network water hammer analysis which follows. The chapter considers series pipes, three pipe junctions, four pipe junctions, valves, pressure-reducing valves, and timevarying boundary conditions. The effects of column separation are not considered and the author cautions the reader for wave speed errors resulting from local pressures below the vapour pressure. Several FORTRAN program listings are given in this chapter. In Chapt. 7 the theory of pumps is reviewed and applied to pump-pipeline systems. The specific cases of pump power failure, with reverse flow and windmilling, and pump start-up are treated. Chapter 8 lists potential problems and refers the reader to specific literature for assistance. Finally, Chapt. 9 introduces control devices such as valves with controller movement, surge relief valves, surge tanks, and air chambers as a means of reducing maximum pressures. Throughout the book the author presents the subject matter to the reader in a clear manner. The reviewer converted several of the listed programs in the book from FORTRAN into BASIC and tested them on a personal computer with good results. The output is generally in tabular form. With few additional statements in the source programs, the output can be stored in arrays for plotting o n a plotter or for graphical output on a printer, which adds significantly to the understanding of the pressure and flow regimes.