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Fanno flow constant area duct Re number

Fanno flow constant area duct Re number

(OP)
I am trying to calculate the friction factor for a Fanno flow in a constant area duct. I know the friction factor is based on Reynolds number however does the Reynolds number not vary along the pipe due to a change in dynamic viscosity? (caused by a decrease in temperature along the pipe). And if so, does this not mean that the friction factor also changes along the pipe?

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