## 2

For pipe containing fittings, the term 4fL/D would be replaced by the sum of the loss coefficients (J] Kf) for all pipe sections and fittings. These equations apply to adiabatic flow in a constant area duct, for which the sum of the enthalpy and kinetic energy is constant [e.g., Eq. (9-50)], which also defines the Fanno line. It is evident that each of the dependent variables at any point in the system is a unique function of the nature of the gas (k) and the Mach number of the flow (NMa) at that point. Note that although the dimensionless variables are expressed relative to their values at sonic conditions, it is not always necessary to determine the actual sonic conditions to apply these relationships. Because the Mach number is often the unknown quantity, an iterative or trial-and-error procedure for solving the foregoing set of equations is required. However, these relationships may be presented in tabular form (Appendix I) or in graphical form (Fig. 9-3), which can be used directly for solving various types of problems without iteration, as shown below.

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