Pressure wave through liquid in pipe

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g_mogni
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Hello,

I'm a bit rusty with my fluid mechanics and can't seem to find the answer anywhere. Basically I have a pressure wave traveling in a liquid at the speed of sound through a pipe of the shape shown in the attachment (basically a semicircle of constant cross sectional area and then a cone of increasing area. At point A I know the wave has planar wavefront. Is there any formula to work out the shape of the wavefront at the end of the cone at point B, which I suppose will have a slight spherical curvature due to the changing cross-sectional size of the pipe?

Thanks
 
Attachments
  • Line drawing of a U-shaped pipe with a constant-width bend on the left and a widening conical section on the right; a blue planar wavefront marked A sits in the left arm with a downward arrow, and a slightly curved blue wavefront marked B sits in the widening cone with an upward arrow.
    wave.png
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Discussion

There isn't really "a formula" that you can use to determine this by just plugging some numbers in. You could solve the system pretty accurately by modeling it with a wave equation and letting the wave propagate through your geometry to see how it ends up. That's quite a bit more involved than just using a formula to spit out an answer, though.
 
Do you happen to know if a software like COMSOL or other similar programs can perform such analysis numerically?

Thanks
 

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