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Unformatted text preview: Fluids Lecture 13 Notes 1. Stagnation Quantities 2. Introduction to Shock Waves Reading: Anderson 7.5, 7.6 Stagnation Quantities Adiabatic stagnation processes An adiabatic stagnation process is one which brings a moving uid element to rest adiabat- ically (without heat addition or removal). The figure a uid element at station 1 in some ow being brought to rest by two hypothetical adiabatic processes. Process A is done by placing a blunt object in the ow, such that the uid element reaches the stagnation point, where V = 0. Process B lets the uid element ow into a large insulated chamber where it will mix with the stationary uid there and thus come to rest. 1 h 1 V h 1 h 1 V 1 h 1 V Adiabatic Process A Adiabatic Process B stag stag V =0 h stag stag V =0 Actual Flow The changes of h and V for either process are governed by the total enthalpy relation 1 h o h + V 2 = constant 2 derived previously. Therefore, we have 1 1 2 h o 1 h 1 + V 1 2 = h stag + 2 V stag = h stag 2 We see that at the end of the stagnation process, h stag is equal to the total enthalpy h o 1 at the beginning. For this reason, the terms stagnation enthalpy and total enthalpy are largely synonymous, although they are two distinct concepts. The total enthalpy h o on the streamline can therefore be measured by setting up an actual stagnation process, typically with a small obstruction like a small-scale version of Process A, and measuring the resulting temperature T stag . One can then calculate h o = h stag = c p T stag ....
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- Fall '05