Use the rough figures in Box 17.4 to estimate the energy released per unit mass in burning the fuel. Does your answer seem reasonable?

Box 17.4.

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BOX 17.4. SPACE SHUTTLE NASA's (now retired) Space Shuttle provides many nice examples of the behavior of supersonic flows. At launch, the shuttle and fuel had a mass ~2 x 106 kg. The maximum thrust, T~3 × 107 N, occurred at lift-off and gave the rocket an initial acceleration relative to the ground of ~0.5g. This increased to ~3g as the fuel was burned and the total mass diminished. Most of the thrust was produced by two solid-fuel boosters that burned fuel at a combined rate of m~ 10,000 kg sover a 2-min period. Their combined thrust was T~2 x 107 N averaged over the 2 minutes, from which we can estimate the speed of the escaping gases as they left the nozzles' skirts. Assuming this speed was quite supersonic (so P < pev²), we estimate that ve~T/m ~2 km s¹. The combined exit areas of the two skirts was A~20 m², roughly four times the combined throat area, A. Using Eq. (17.9) with y~ 1.29, we deduce that the exit Mach number was Me~ 3. From T~ PevA and Pe= Cepe/y, we deduce the exit pressure, Pe~T/(M²A₂)~8 × 10¹ N m2, about atmospheric. The stagnation pressure in the combustion region was [combine Eqs. (17.2a), (17.2d), and (17.8)] A~A[1+2 P₁~ Pe (x - 1)M² 2 ~ 35 atmospheres. (1)