ESDU 81004 gives three Mach number dependent functions, the momentum function and alternative forms of the mass flow function, which are useful in many one-dimensional duct flow problems. The use of these functions is general since friction, area change and heat exchange effects are simultaneously or separately accommodated. The functions are plotted against Mach number, for various values of specific heat capacity ratio. ESDU Aero 00.03.05 and ESDU Aero S.00.03.07 give flow relations for steady one-dimensional isentropic flow. These flow relations may be applied to non-isentropic duct flow to evaluate local conditions provided that proper account is taken of any changes that may occur in total pressure and total temperature along the duct. Information in ESDU Aero 00.03.05 and ESDU Aero S.00.03.07 may often be usefully applied in conjunction with ESDU 81004.