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An explosion is a rapid increase in volume and release of energy in an extreme manner. A blast wave in fluid dynamics is the pressure and flow resulting from the deposition of a large amount of energy in a small very localised volume. The equation for a Friedlander waveform describes the pressure of the blast wave as a function of time:

$$P(t)=P_oe^{-\frac {t}{t^*}}(1-\frac {t}{t^*})$$ where P$_o$ is the peak pressure and t$^*$ is the time at which the pressure first crosses the horizontal axis (before the negative phase).

My Question: Why does the pressure temporarily drop below ambient after the wave passes?

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Ehh... what exactly do you need to know? –  Deer Hunter Jul 16 '13 at 4:51
    
Are you asking why the pressure temporarily drops below ambient after the initial blast wave passes? –  Michael Brown Jul 16 '13 at 5:33
    
Yes thats what i want to know –  Neo Jul 16 '13 at 6:09
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up vote 4 down vote accepted

If you start with a finite amount of gas in the inner sphere and then deposit a massive amount of energy, the molecules of the gas begin moving rapidly outwards and piling up, creating the blast wave. However, the rate at which the gas is moving outwards may not be balanced by the amount of gas molecules being created by the explosive. If this is the case, then the pressure must decrease below ambient as the molecules are pushed outwards with the blast wave.

You can see this in videos of blast waves. The initial wave continues to move outwards, but the smoke/dirt/debris caused by the explosive will move outwards initially, then inwards as the lower pressure region sucks it back in towards the center. There is actually considerably banging that goes on where the low pressure behind the blast wave moves inwards and outwards until it relaxes back to atmospheric pressure.

Here is a great video that shows the blast and resulting banging as the pressure relaxes.

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