36 
90, For comparison with case 3 it is convenient to express the results 
for the present case 2 in terms of the fraction of the energy of the 
incident pulse which is communicated to the plate. Writing, 
] 
= det 
energy comunicated to unit area of plate --. (37) 
2 
Po 
Qe Sonn = energy in the pressure pulse, incident on... (38) 
f unit area of the plate 
then from equations 35 and 32 it follows that 
hee coe coe eee eco eve coe eoe (39) 
Water exerts no tension on plate and cavitates after plate leaves water 
914. Consider the general case where the water cavitates at some finite 
tension. The conditions in the water at various stages of the motion 
are then illustrated diagrammatically in fige 17 which shows in each stage 
the incident pulse, lettered P to X, moving to the left and the reflected 
pulse, lettered P' to U', moving to the right; the latter is plotted 
negatively since it is easier to see at a glance the resultant pressure 
or tension as the difference rather than as the sum of the ordinates of 
two curves. Fig, 17a illustrates the conditions prior to the plate 
leaving the water, the net pressure, given by the difference between 
the curves PQRST and P'Q'R', being positive everywhere. (Fig. 17a 
applies also for the previous cases 1 and 2). 
92, Fige17b illustrates conditions at the instant the plate breaks away 
fron the water, the net pressure being zero at the plate and positive 
elsewhere. Fige17c illustrates the conditions after this instant but 
prior to any cavitation in the water. The water 1s subjected to a net 
tension over the range OL and to ea net pressure for greater distances 
from the original plate position The plate is now ahead of the water, 
that is to the left of AB, with a gap between The abrupt change of 
slope at T' in fige17c corresponds to the change-over as the plate leaves 
the water, from reflection of the incident pulse at the accelerating plate 
to reflection at the subsequent free water surface AB. (The conditions 
shown in fig. 17c represent also the water conditions in case 2)- 
93. Fige17c will continue to represent the events in ths water until the 
greatest net tension T'S exceeds the tensile strength of the water. The 
resultant particle velocity in the water is represented (to arbitrary 
scale) by the sum of the full and broken curves infig.17- In particular, 
therefore, the water to the left of T'S in fige17c is moving to the left 
and if T'S becomes just greater than the tensile strength of water, the 
layer to the left will break away and follow up the plate. 
94. For a finite tensile strength of water, this first layer will be of 
finite thickness, but due to the shape of the curves for the incident and 
reflected pulses, subsequent layers of -infinitesimal thickness will be 
projected after the plate and in effect a "cavitation front" is propagated 
back through the water away from the original plate position The 
subsequent conditions following such cavitation in the water are illustrated 
in fig. 17d where the cavitation front at position CD separates the water on 
the left, which has cavitated and is following up the plate, from the 
water on the right which has not yet cavitated 
