(48.18). Using (55.3) in (55.lb) or (55.2), we obtain (du/dt)+ (u * a)((%dd.x)= o.(55.5) Similarly, by inverting the function p(u), we can write the continuity equation as (dp/dt) +[p(du/dx) + U](dp/dX)= O, which, from (55.3), implies(dp/dt) + (u + a)(dp/dx) = O. Equations (55 .5) and (55.7) yield general solutions ofu =Fl [x-(u+a)t] and p= F2 [x-(u*a) Because p = p(u), p = p[p(u) In the case illustrated in Figure 56. 1, v, < @ and VI= O, hence UI >0, as is u" . THE CONSERVATION LAWSIn the frame of the shock the flow is steady, hence the equations of continuity, momentum, and energy (again ignoring viscosity and conduction) reduce to (56.4) and (p, V) plane, either (56.13) or (56.14) defines a unique curve P(V) = f (p,, V,, V), called the Hugoniot cur-ue, passing through (p,, V,)

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