Kinetic energy (KE): it is the energy of fluid by virtue of its motion and is

(4)

                                                                                                                    
In equation 4 V is the velocity of fluid. Increase in K E /unit mass as the fluid flows from position 1 to 2 is

(5)

                                                                                                             
Pressure energy:  It is the energy possessed by the fluid because it enters and exits at some pressure.

(6)

                                                         
Mechanical energy (M): This energy may be added to the flow from the outside by means of a pump or fan.

Self expansion work is the mechanical work that 1 kg of fluid does on the fluid surrounding as it expands in passing through the system.-
.  
                                                                              
Friction:  It is the conversion of mechanical energy into heat due to the movement of the fluid.
Putting all energies together

(7)

Since

(8)

By 7 and 8 and after rearrangement we get