Page 264 - Dynamic Loading and Design of Structures

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Figure 6.3 Spherical shock wave.

6.2.2 Shock wave parameters
Most explosions, after propagating a short distance, produce a spherical shock wave of
2
surface area A=4π (Figure 6.3).
r
The characteristics of the spherical air shock are as follows:
2
(a) The energy of the shock front/unit surface area decreases with r (inverse square law).
(b) The peak overpressure p decreases with distance r from the explosion and eventually
s0
reduces to a sound wave (Figure 6.4).
(c) The velocity of the shock front u is given by:

where us=340 m/s is the sound velocity in air for normal conditions at sea level and
2.
atmospheric pressure p0=0.1 N/mm The different units used for pressure are 1
2
N/mm =1 MPa=145 p.s.i.=10 bar.
(d) t is the positive duration of the shock wave which increases with distance from the
dp
explosion because higher pressures travel faster (Figure 6.5).
(e) ps is the overpressure which decays with time at a fixed location depending on ps0 and tdp
(Figure 6.6).
(f) v is the velocity of the air particles behind the shock front as they move radially away from
the explosion during the positive phase (e.g. for p s0= 3p then v=300 m/s) and towards the
0
explosion in the negative phase.
(g) pd is the dynamic pressure where ρ=air density.