By H. Daneshyar

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When P B dr0P5 below this value (regime IV), oblique expansion waves are formed in the reservoir around the exit of the duct and a free streamline is formed; again flow in this region is not amenable to one-dimensional treatment. In both regimes III and IV the flow pattern in the duct is independent of the back pressure pB and is the same as for the design condition. All adjustments to back pressure are made in the reservoir near the duct exit. Thus P E/ p in regimes III and IV depends only on the ratio of 0 the throat area to the exit area of the duct.

Flow behind the portion of the shock facing the inlet first diverges and then converges to give M = 1 at the throat. (Note that the bending of the streamlines can only occur for a shock oblique to the flow). The divergence of the streamlines behind the shock causes some of the air in the path of the duct to be spilled around its lips, thus reducing the mass flow rate. If the throat area is further reduced, the shock moves further upstream and causes more spilling of the flow. Now if the above procedure is reversed, that is the throat is expanded again, there will be a hysteresis effect.

16) the net force on the walls in the opposite direction of motion is - ~ 1) (12 - ra(A2 -A1) In the case of the rocket tube motor (Fig. 17) Isentropic Flow Net thrust = 1 2 - p A a 2 =r A V 2 2 2 2 + A (p 2 2 - p). 3 is only a function of p o o and can be tabulated for specified values of Mach number (Table 2). The ratios can also be given in graphical Mach number and and U L2 T form (Fig. 5) . The tables and graphs can be used for engineering calculations and their use is usually preferred to using the equations directly because in most cases solution of the equations is tedious.