On the Period of Water Pressure Oscillation in Composite Closed Conduit

Abstract

In the analysis of water hammer in a composite closed conduit, it is transformed into an equivalent simple conduit with the following mean elastic wave velocity a_m0:
a_m0=∑L_i/∑(L_i/a_i)
where L_i and a_i are the length and the wave velocity of the i-th conduit respectively. In the simple conduit system, which is connected to a large reservoir at one end and to a closed valve at the other, the relation between the period of pressure oscillation T₀ and the wave velocity a_m0 is given by
T₀=4·∑L_i/a_m0
However, it is clarified by a simulation that this relation does not exist in composite conduits.
If the conception-the water hammer is a phase of energy exchanging process between kinematic and elastic energy-is introduced, then the following equations of mean velocity a_m and the period T are deduced:
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where V_i is the volume of the i-th conduit, and f_e and (f·f') ₀ are the coefficients expressing areal changing effect and wave velocity changing effect respectively. From this theory it is shown that the conventional theory is deficient and the inconsistency of it is removed.
Furthermore, the equations by which f_e and (f·f') ₀ are approximately estimated on a two-conduit system are deduced, and appropriateness and adaptability of this theory are examined using simulation. At the same time, the structural characteristics in factors bringing about water hammer are also discussed.