Abstract
The author supplements the pioneer work of Prof. F. M. Wood in applying operational methods to the study of water-hammer phenomena. The Heaviside calculus is replaced by the Laplace-Mellin transformation together with the elementary theory of functions of a complex variable. This substitution facilitates interpretation of a much wider range of operators, is believed to be better adapted to problems starting from a steady-state system in motion, and permits working directly with total pressures and velocities instead of surge pressures and velocities. This third feature operates to eliminate ambiguity concerning reflection coefficients at junction points in branched-conduit problems. When the effect of friction is not included, results are given in the form of simple trigonometric series of rapid convergence. When the abscissas of the two terminal sections of the conduit are inserted in these formulas, the resulting expressions are, in many cases, Fourier representations in the time variable of well-known periodic step or saw-tooth functions. In such instances, almost no computation work is required; it is unnecessary to sum the series, as the value of the summation may be taken at a single reading from a graph of the function, one plot of such a function serving for all particular cases within its domain. In cases where the effect of friction is included, a standard table of Bessel functions, used in conjunction with the formulas developed, affords easy and comparatively rapid solution.
