ENGINEERING STRUCTURES 143 



end of the pipe the motion is suddenly stopped and the 

 pressure rises to p= 48 v Ibs. per square inch. After a further 

 interval, 21 -r V p seconds, that portion of the column, of length 

 2/, nearest the closed end is at rest under this pressure, the 

 rest of the pipe being under normal pressure and zero velocity. 

 Instantaneously, however, the end of this stressed column, 

 which is more remote from the closed end, rebounds with velo- 

 city v ~ 2 and pressure 24 v Ibs. per square inch, layer after 

 layer following suit, until after a further interval, 21+ V p 

 seconds, this is moving under this state of pressure and 

 velocity towards the open end. The dilatation, under this 

 tendency to retrograde motion, of those layers in contact 

 with the closed end, causes the pressure to fall to normal, 

 and a state of normal pressure and of zero velocity is now 

 reflected to the open end, following the preceding pressure- 

 velocity wave, whose state occupies a length, 2?, of the pipe 

 at each instant. When this former wave reaches the open end 

 the pressure falls to that obtaining at this point, the velocity 

 increases to l v? and a wave of normal pressure and of velocity 

 ' v ' (towards this end) is reflected towards the closed end. On 

 arriving at that portion of the pipe in which the pressure is 

 normal and the velocity zero, the pressure becomes 24 i; Ibs. 

 per square inch, and the velocity v -I- 2 and a wave conveying 

 this state over a length 21 -j- V f of the pipe, travels on towards 

 the closed end. On its arrival the pressure becomes 48 v Ibs. 

 per square inch, the velocity zero, and this state is reflected 

 to the open end again. Arriving here, the pressure becomes 

 suddenly normal, the velocity becomes v towards the closed 

 end, and the whole cycle is repeated. The true pressure-time 

 diagrams, as obtained respectively at this end, and at a point V 

 from the end would then appear as in Fig. 5, a and 6. 



Since in a number of the jet experiments /', the distance of 

 the indicator from the closed end of the pipe, was greater than 

 21, the theoretical pressure diagram at this point in such cases 

 would be as indicated in Fig. 5, c, the maximum pressure at 



