A gas flow control problem

A mathematical formulation of the velocity control problem for the flow of an ideal gas in a fixed-length channel is presented for the case of zero friction and for the case which includes friction. The work of friction is found to depend only on the specific volume and pressure; for either case studied, the controls are the gas temperature and the channel wall temperature. The specific entropy is found as a function of the controls and of time. Given the specific entropy and the temperature as functions of time and using the equations of state, the specific volume, pressure, and specific internal energy are determined. The velocity and the channel section can be found using given expressions.