By George Emanuel
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The idealization of a shock as a discontinuity in the flow is thus appropriate. 2, and h2. With four unknowns and three equations, it becomes necessary to make a statement about the thermal and caloric states of the gas. 3c) (1) (2) Fig. 1 One-dimensional flow in a constant area duct; the double line is a normal shock wave. 4) where Ml is referred to as the shock Mach number. To begin with, let us manipulate the energy equation using Eq. 6) Thus, the stagnation temperature does not change across a steady shock wave, a result we might have anticipated from Eq.
The initial pressure and density are p^ and p^, respectively. On the left side of 32 GASDYNAMICS: THEORY AND APPLICATIONS the duct is a diaphragm that starts to vibrate sinusoidally at time t = 0. , and p change from their initial values. We assume that the magnitude of the displacement of the diaphragm from its neutral position is small. As a consequence, the gas experiences a small perturbation of its state, and we can write V=V'(x,t), >'(*, 0, where a prime denotes a perturbation quantity. Based on the earlier discussion, substitute 1 p e = ——r y-1 — p A = const, into Eqs.
We are to determine the mass flow rate, the Mach number at each section, and the diameter of the downstream section. Since the duct is insulated, the flow is assumed to be isentropic. The upstream and downstream sections are denoted by subscripts 1 and 2, respectively. Since the pressures pl and p2 are known, the isentropic relation, Eq. 8 K ^ Hence, Ml is given by l ~ " . 8 ~ Although not asked for, ro and pQ are useful. They are given by l + l^M? 017atm To find M2, we solve Eq. 9) as follows: \(Y-D/Y ,Pi.