8.2.2.1 The square shot sleeve

Since Garber's model never work Brevick and co-workers go on a ``fishing expedition'' in the fluid mechanics literature to find equations to describe the wave. They found in Lamb's book several equations relating the wave velocity to the wave height for a deep liquid (water)<sup>8</sup>. Since these equations are for a two dimensional case, Brevick and co-workers built it for a squared shot sleeve. Here are the equations that they used. The ``instantaneous'' height difference ( ) is given as

(8.11)

This equation (), with little rearranging, obtained a new form

(8.12)

The wave velocity is given by

(8.13)

Brevick introduces the optimal plunger acceleration concept. ``By plotting the height and position of each incremental wave with time, their model is able to predict the `stability' of the resulting wave front when the top of the front has traveled the length of the shot sleeve.''<sup>9</sup>. They then performed experiments on this ``miracle acceleration ¹⁰.''