Brode’s equation

Four methods are used to estimate the energy of explosion for a pressurized gas Brode s equation, isentropic expansion, isothermal expansion, and thermodynamic availability. Brode s method21 is perhaps the simplest approach. It determines the energy required to raise the pressure of the gas at constant volume from atmospheric pressure to the final gas pressure in the vessel. The resulting expression is... 

The estimate of the explosion energy suffers from the same type of inconvenience of Brode s equation, and the analogy of the explosion of a pressurized gas vessel to a TNT one appears improper in the near field, since the vessel cannot be regarded as a point source. In this case, the correction method uses a virtual distance from the explosion center (Petes, 1971), to fictitiously move the explosion centre with respect to the surface of the expanding gas. The maximum overpressure of the shock wave, i.e. that at the contact surface between the initial expanding gas sphere and the air, is evaluated as (Baker et al., 1983 Prugh, 1988) ... 

In Brode s equation, which is used in Baker s model, larger values of the heat capacity ratio result in lower explosion energies. As highhghted before, since larger values of the heat capacity ratio correspond to increasing pressures, from this point of view, the direct influence of the burst pressure on the explosion energy in the Baker s model is somehow counterbalanced by the variability of / and this explains the slower increase of the explosion energy with respect to that calculated with the Brown equation. 

Figure 1. Explosion energy for a 10 m vessel at 20°C, according to Brode s and Brown s equations.

The total energy of a vessel s contents is a measure of the strength of the explosion following rupture. For both the statistical and the theoretical models, a value for this energy must be calculated. The first equation for a vessel filled with an ideal gas was derived by Brode (1959) ... 

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