Now, By manipulating equation 11 and integrating bothsides we get,  formula_28  L* is the length from some arbitrary point where Mach number is Ma. At the sonic region, Ma=1. The integration results in the following equation :  formula_29  Where f- is average friction factor from x=0 to L*. Here D is the diameter of circular duct; in cases where the duct is not of circular cross section D=(4*area)/perimeter. Choking of duct is basically reduction of duct mass flow. The flow conditions change if the actual length L is greater than the predicted maximum length L*, and there are two classifications :  If L > L*(Ma1), the flow slows down until an inlet Mach number Ma2 is reached such that L = L*(Ma2). The exit flow is sonic, and the mass flow has been reduced by frictional choking. Further increases in duct length will continue to decrease the inlet Ma and mass flow. Friction have a very large impact on supersonic duct flow. Even an infinite inlet Mach number will be reduced to sonic conditions in only 41 diameters for f = 0.02. Consider an example inlet Ma = 3.0 and f=0.02. For this condition L*=26 di ameters. If L is increased beyond 26D, the flow will not choke but a normal shock will form at just the right place for the subsequent subsonic frictional flow to become sonic exactly at the exit. Eventually, a very long duct will cause the feednozzle throat to become choked, thus reducing the duct mass flow. Thus supersonic friction changes the flow pattern if L > L* but does not choke the flow until L is much larger than L*.