Hydraulics of Pipe Lines

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27) will depend on the size of the chamber relative to the other characteristics of the case. The smaller the chamber the greater will be the amplitude. With a chamber of sufficient size the swing beyond final values becomes negligible, and the movement is then sensibly dead beat.
23. TREATMENT OF SURGE CHAMBER EQUATIONS Differential equations of the form presented in (6), (7) or (8), (9), and representing a dampened oscillation in which the retarding force varies as the square of the velocity,
... do not seem to permit of direct solution by any known mathematical means. Under these conditions the following courses are open : 1. The treatment of restricted or special cases which may admit of mathematical solution. This represents a partial solution of the equations.
2. The treatment by approximate methods involving some departure from the exact relations implied by the equations, and thus making possible a solution by direct mathematical means.
3. The treatment of the equations as they stand or in simplified form by methods of approximate numerical integration.


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