General polytropic flow

For steady flow of an ideal gas between points 1 and 2, distance L apart, in a pipe of constant cross-sectional area in which no shaft work is done, the energy equation is given by equation 6.19. For the general case of polytropic flow, from equation 6.27, the equation of state can be written as... 

Equation 6.49 is the general equation for polytropic flow of an ideal gas in a horizontal pipe with no shaft work. On putting k = 1, equation 6.38 for isothermal flow is obtained. 

The numerical behaviour of these flow functions is shown in tabular and graphical forms below. Table 5.1 shows three instances for the general, polytropic case ... 

Real compression processes operate between adiabatic and isothermal compression. Actual compression processes are polytropic processes. This is because the gas being compressed is not at constant entropy as in the adiabatic process, or at constant temperature as in the isothermal processes. Generally, compressors have performance characteristics that are analogous to those of pumps. Their performance curves relate flow capacity to head. The head developed by a fluid between states 1 and 2 can be derived from the general thermodynamic equation. 

Under adiabatic conditions heat flows have to be modelled accordingly with respect to the mass balances. For exothermic reactions usually a stimulation of the chemical reaction is required due to the higher energy level at the beginning of the reaction. In general, the interactions between heat and mass balances are more difficult to model. More complicated cases occur when both conditions are mixed, i.e. under polytropic conditions. Here, solutions for heat and mass balances are hardly available analytically. Instead,... 

---