SURFACE AND OTHER EFFECTS 



406 



(10.9) P = P, + P, = p^re-0 + |>+ i-±|6-O-0/« 



2/3 

 1-^ 



e-Hi- 



t > 



The quantity ^, which expresses the effect of the plate on the pressure 

 in the water, is zero for an infinitely thick plate (m — > oo ) and infinite 

 for a plate of zero mass (i.e., a free surface), and Eq. (10.9) for pressure 



Fig. 10.4 Contours of equal pressure in front of accelerated free plates for 

 two different relative inertias. 



P is easily seen to reduce to the results of section 2.8 in these cases. In 

 intermediate cases, the solution must be carried out explicitly. 



It is evident, however, that for sufficiently large jS, P will become 

 negative at points in the fluid and may acquire large negative values 

 for a sufficiently light plate or long duration of the incident wave. This 

 corresponds to a rarefaction wave reflected from the accelerated surface 

 of the plate, and the water in front of the plate may therefore be called 

 upon to withstand large tensions. If, instead, the water cavitates, the 

 subsequent motion of the plate will be modified. 



The pressure field in any particular case can conveniently be illus- 

 trated by plotting isobars (contour lines of equal pressure) as a function 

 of position and time. This is done in Fig. 10.4a^ for the case ^ = 4.0, 



•* The data for these plots are taken from Reference (31). 



