By Gordon P. Blair
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In their travel along the pipe, the front and the tail will keep station with each other in both time and distance. However, at the front of the wave, all of the pressure points between it and the peak are travelling faster and will inevitably catch up with it. Whether that will actually happen before some other event intrudes (for instance, the wave front could reach the end of the pipe) will depend on the length of the pipe and the time interval between the peak and the wave front. Nevertheless, there will always be the tendency for the wave peak to get closer to the wave front and further away from the wave tail.
This is the classic echo situation, so it is no surprise to discover that the mathematics dictate that the reflected pressure wave is an exact image of the incident wave, but travelling in the opposite direction. The one certain fact available, physically speaking, is that the superposition particle velocity is zero in the plane of the closed end, as is shown in Fig. 5(a). From Eq. 2) From Eq. 3) Hence, Pr=Pi. 2 Reflection of a pressure wave at an open end in a pipe Here the situation is slightly more complex, in that the fluid flow behavior is different for compression and expansion waves.
Anywhere in an unsteady flow regime where a pressure wave in a pipe is incident on a pressure filled space, box, or cylinder, the following method is applicable to determine the magnitude of the reflected pressure wave. The solution of the gas dynamics of the flow must include separate treatments for subsonic inflow, sonic inflow, subsonic outflow and sonic outflow. 6). 7). A complete description of the solution is out of place in this book, as the theoretical solution would occupy almost a book in itself, but the result of that solution is presented in graphical form in Fig.