Fanno flow
![Figure 1 A Fanno Line is plotted on the dimensionless H-ΔS axis.](/Images/godic/202501/12/Fanno14346.PNG")
![Figure 2 Common thermodynamic property ratios plotted as a function of Mach number using the Fanno flow model.](/Images/godic/202501/12/Fanno_Properties4346.PNG")
![Figure 3 A supersonic nozzle leading into a constant area duct is depicted. The initial conditions exist at point 1. Point 2 exists at the nozzle throat, where M = 1. Point 3 labels the transition from isentropic to Fanno flow. Points 4 and 5 give the pre- and post-shock wave conditions, and point E is the exit from the duct.](/Images/godic/202501/12/Fanno_flow_through_a_nozzle4347.png")
![Figure 4 The H-S diagram is depicted for the conditions of Figure 3. Entropy is constant for isentropic flow, so the conditions at point 1 move down vertically to point 3. Next, the flow follows the Fanno line until a shock changes the flow from supersonic to subsonic. The flow then follows the Fanno line again, almost reaching a choked condition before exiting the duct.](/Images/godic/202501/12/H-S_graph_of_a_Fanno_flow4347.png")
Fanno flow refers to adiabatic flow through a constant area duct where the effect of friction is considered. Compressibility effects often come into consideration, although the Fanno flow model certainly also applies to incompressible flow. For this model, the duct area remains constant, the flow is assumed to be steady and one-dimensional, and no mass is added within the duct. The Fanno flow model is considered an irreversible process due to viscous effects. The viscous friction causes the flow properties to change along the duct. The frictional effect is modeled as a shear stress at the wall acting on the fluid with uniform properties over any cross section of the duct.