U cos C h

The difference between the two solutions depends on the magnitude of the quantity —c. Analysis of strong ground motions of the past earthquakes seems to indicate that frequencies of most of the significant harmonic components lie in the range 1 < u < 120 rad/sec. Thus, the largest value of —C may be taken as 6.82 x 10-3(u = 1, C = 4720fps). However, such low frequency harmonics contribute little to the response in the case of typical reservoir depths encountered, because natural frequencies for the reservoir are rather high: e.g. for a 300 ft deep reservoir u1 = 24.72 radians per sec. The magnitude of —C for harmonics of significance is therefore considerably less than 6.82x10-3, and errors introduced by dropping terms involving —c will be small, except possibly near the free surface. Therefore, equation2.42 is sufficiently accurate.

Most investigator have ignored the waves that may be generated at the free surface of water. For compressible fluid, and harmonic excitation it was found that the error ,e , introduced by ignoring surface wave, varies as follows:

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