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APPENDIX III. 
MISCELLANEOUS. 
(29) Some general Points in the Theory and Use 
of Pressure Gauges. 
There is » general question which arises in connexion with any form of gauge for measuring the 
pressure ina pressure wave. The measurement required is the pressure that would exist in the water if 
the gauges were absent; to what extent are the gauge results vitiated by the modification of pressure 
due to the presence of the gauge? ‘The presence of the gange modifies thc pressure in two ways. In 
the first place the gauge as a whole, regarded as an approximately rigid heavy body, increases the pressure 
on its front face (the side towards the oncomiug wave) by reflection, and diminishes the pressure on its 
back face by shadowing. The seriousness of this effect depends on the relation betweon the size of the 
gauge und the thickness of that part of the pressure wave which it is supposed to measure. As regards 
the present gauges the effect will be most serious in the case of Type GF (Fig. 37); the linear dimensious 
of this gauge average about 3 inches and it has a {ime-constant of 10-4 second, corresponding to a 6-inch 
thickness of the wave in the water. The question was examined experimentally for this type of gauge 
by putting down 3 gauges near one another at equal distances from the charge, the working face of the 
first gauge being directed towards the charge, of the second at right angles, and of the third away from 
the charge ; in three experiments of this kind, with gauges 40 feet away from 300-lb. charges of amatol 
or T.N.T., the pressures recorded were in the ratio :— 
105 : 100 : $5 
105 (2100: 2/97 
108 : 100 : 96 
Average - - - 106 : 100 : 96 
These results show that so far as the present gauges are concerned the effects of reflection and 
shadowing are not large even in the most unfavourable case ; it must also be remembered that throughout 
the investigation, with a few exceptions, the gauges were hung in the second of the above three positions, 
with the axis of the gauge at right angles to the direction of the charge, so that neither reflection 
nor shadowing would come into play to any appreciable extent. 
In the second place every gauge has a part which yields to the pressure ; how far is the pressure in 
the water reduced by the relief thus afforded to it? In dealing with this question it is convenient to have 
in mind an actual example ; take the case of a G gauge (Fig. 34) at a distance of 50 feet from a 300-lb. 
amatol charge; this gauge has @ piston 3 inches long and 4 inch in diameter, with a free travel of 
2 inches before it hammers the copper ; from the moment when the pressure wave reaches it the piston 
moves with a continually increasing velocity until, after about five-thousandths of a second, it reaches the 
end of its travel with a velocity of about 50 feet per second. The movement of the piston propagates 
a secondary tension wave which spreads in all directions with the velocity of sound in water, and at any 
moment the pressure at a given point in the water is the algebraic sum of the pressure that would exist 
if the gauge were absent and the tension due to the movement of the piston. What we have to find is 
the extent to which the pressure is relieved at the mouth of the piston hole ; this can be approximately 
estimated as follows: under a steady pressure p, water is forced through an unobstructed aperture with 
a velocity— 
van/2, or V =570Vp, 
Pp 
if V is expressed in feet per second and p in tons per square inch ; conversely, if a piston is withdrawn 
into a gauge with velocity V the pressure at the mouth of the piston hole will be relieved by an amount 
p=31 x 1077 V*._ In the example stated above V is only 50 feet per second, so that the relief of pressure 
is less than -Ol ton per square inch, which is too small to be of any consequence. Taking the whole 
range of the experiments the velocity of the pistons was generally of the order of 50 feet per second or 
less ; in a few instances it was of the order of* 100 feet per second, or even a little higher, but this was 
only when the driving pressure was very great, so that the relief of pressure was still proportionately small. 
It may be concluded therefore that the movement of the piston does not reduce the driving pressure ia any 
serious degree. The above way of looking at the matter is only justified when the diameter of the piston 
is small compared with the thickness of wave measured by the gauge, as it always is in the present gauges ; 
if the diameter of the piston were large compared with the thickness of wave measured by the gauge 
entirely different considerations would apply, and the effect of the velocity of the piston in reducing the 
pressure would be far greater. 
In calculating the results given by the gauges the pistons are assumed to be rigid. ‘This assumption 
is roughly justified by the fact that the time required for a pressure wave to travel from one end of the 
piston to the other is always very small compared with the time during which the pisten is receiving 
momentum from the external pressure. ‘he most unfavourable case is the GX gauge (Fig. 35) with 
f-inch pistons; in this case the time required for a pressure wave to trayel from one end of the piston 
to the other is abont four millionths of a second, while the time during which the piston is receiving 
momentum from the external pressure is of the order of 2 x 1074 second, or 50 times as long. It is 
perhaps desirable to go into this matter a little more fully. The movement of the piston at any moment 
can be resolved into (1) a uniform movement of translation, with a momentum equal to the time-integral 
of the force that has acted on the end of the piston, and (2) a state of distributed momentum, of which 
