By George Emanuel

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Additional resources for Gasdynamics : theory and applications

Example text

5283. The curve for A/A* in the figure will be discussed in the next section. The dynamic pressure pV2/2 is often used in incompressible flow. In the next example, we compare p + pV2/2 with pQ. Example 1 Compare p + pV2/2 with pQ when the Mach number is small, and determine the incompressible counterpart to TQ. We begin with the perfect-gas energy equation which holds whether the flow is compressible or incompressible. Thus, the incompressible counterpart of T0 is T. By way of contrast, for an incompressible flow, Eq.

T? 44 GASDYNAMICS: THEORY AND APPLICATIONS which agrees with Q when M 2 is small. Since higher-order terms are positive, we observe that pQ > Q. 3 AREA AND MASS FLOW RATE Our immediate task is to relate the area A(x) to the Mach number and to determine the mass flow rate m. T&TM (4-11) For Eqs. 10), the reference condition is a stagnation condition, where M = 0. Here, we obtain a more convenient reference condition by setting Af = 1. , when M = 1. Since the mass flow rate is a constant, it is not altered by this choice.

7), we have de= -pdv The differentials de and dv are for a particle of fluid that is in motion and whose state is changing with time. These differentials, therefore, represent 30 GASDYNAMICS: THEORY AND APPLICATIONS changes previously denoted by the substantial derivative; hence, This form for conservation of energy does not explicitly contain a term for the kinetic energy of translation. However, we can obtain an equation for the total energy per unit mass e 4- F2/2 by adding to Eq. 10a) V times Eq.