We have stated earlier that shock waves occur in supersonic flows a stationary normal shock such as shown in Fig 8. 3 does not occur in subsonic flow. That is, Eqs. (8.59),(8.61), (8.65), and( 8.67), the upstream mach number is supersonic, Mi>l. however, on a mathematical basis, these equations also allow solution for mi<l These equations embody the contiunity, momentum, and energy equations, which in principle do not care whether the value of M, is subsonic or supersonic. Here is an ambiguity which can only be resolved by second law of thermodynamics 我们在前面已经指出,激波出现在超音速流中;图8.3所示的精 制的正激波在亚音速流中不可能出现。也即是,关系式(8.59, (861),(8.65,和(867)中上游马赫数必须是超音速的:必有M1≥1 然而,从纯数学的观点看,这些由连续、动量、能量方程推导出 的关系式在理论上并没有限定M1一定要大于1,即上游流动一定 是超音速的。这种多解性只有借助于热力学第二定律来解决。We have stated earlier that shock waves occur in supersonic flows; a stationary normal shock such as shown in Fig.8.3 does not occur in subsonic flow. That is , Eqs. (8.59),(8.61),(8.65), and (8.67), the upstream Mach number is supersonic, M1≥1. However, on a mathematical basis, these equations also allow solution for M1≤1. These equations embody the contiunity, momentum, and energy equations, which in principle do not care whether the value of M1 is subsonic or supersonic. Here is an ambiguity which can only be resolved by second law of thermodynamics. 我们在前面已经指出，激波出现在超音速流中；图8.3所示的精 制的正激波在亚音速流中不可能出现。也即是，关系式(8.59), (8.61), (8.65), 和 (8.67)中上游马赫数必须是超音速的；必有 M1≥1。 然而，从纯数学的观点看，这些由连续、动量、能量方程推导出 的关系式在理论上并没有限定 M1 一定要大于1，即上游流动一定 是超音速的。这种多解性只有借助于热力学第二定律来解决