Abstract
This paper presents an analytical study of the stationary response of a liquid loaded on its free surface by an ideal pressure step moving in a constant direction at a constant velocity. The acoustic pressure in the liquid is found, in four different examples, by means of the Fourier Transform. Two loading regimes are considered; subsonic and supersonic. Two configurations of liquid domains are also studied, the first one is a half infinite space while the second one is bounded by a rigid bottom at a finite depth. For the two supersonic cases, a simple reasoning based on the existence of a front of discontinuity in the liquid and on the property of reflection of waves confirms the result of the mathematical investigations. The results obtained for the steady state case are of intererest, even when the loading is not exactly stationary, such as the presure produced by an explosion occurring in the vicinity of the surface of a liquid. Two numerically resolved examples are presented, which confirm this assumption.For the two supersonic cases, a simple reasoning based on the existence of a front of discontinuity in the liquid and on the property of reflection of waves confirms the result of the mathematical investigations.The results obtained for the steady state case are of intererest, even when the loading is not exactly stationary, such as the presure produced by an explosion occurring in the vicinity of the surface of a liquid. Two numerically resolved examples are presented, which confirm this assumption.
Highlights
The objective of this work is to determine, under rational hypothesis, the analytical formulas for the pressure induced in a liquid by a loading pressure wave travelling over its surface at a high uniform speed and amplitude
Such loading pressure may be typically produced by a detonation
The loading pressure starts at a definite time and the observations are made when the pressure front has traveled over a distance of 100 meters
Summary
The objective of this work is to determine, under rational hypothesis, the analytical formulas for the pressure induced in a liquid by a loading pressure wave travelling over its surface at a high uniform speed and amplitude. Such loading pressure may be typically produced by a detonation. Experimental results of the effect of a moving shock wave over the surface of a liquid are presented by Borisov et al [2] They consider the detonation of a gaseous explosive mixture confined in a tube partially filled with liquid. This theoretical solution is obtained by Fourier transforms, either in the subsonic or in the supersonic case
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