## 5.3. Hugoniot Relations and the Hydrodynamic Theory of Detonations

If one is to examine the approach to calculating the steady, planar, 1D gaseous detonation velocity, one should consider a system configuration similar to that given in Chapter 4. For the configuration given there, it is important to understand the various velocity symbols used. Here, the appropriate velocities are defined in Figure 5.1. With these velocities, the integrated conservation and static equations are written as

${\rho}_{1}{u}_{1}={\rho}_{2}{u}_{2}$

(5.1)

${P}_{1}+{\rho}_{1}{u}_{1}^{2}={P}_{2}+{\rho}_{2}{u}_{2}^{2}$

(5.2)

${c}_{p}{T}_{1}+\frac{1}{2}{u}_{1}^{2}+q={c}_{p}{T}_{2}+\frac{1}{2}{u}_{2}^{2}$

(5.3)

${P}_{1}={\rho}_{1}R{T}_{1}(\text{connects}\text{known}\text{variables ...}$

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