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## Homework Statement

In our fluid mechanics class we were taught that we could use the following equation to solve for the Darcy friction factor f:

To do this by hand:

1. Guess a value for 1/sqrt(F), guess 3

2. Get the right hand side result of the equation using 3

3. Use that result for the next value of 1/sqrt(F)

4. Continue using the result for the next value.

5. To find F, just divide one by that value squared.

This iterative approach works but I am not too sure why. Can anyone explain why it works? I'm guessing it requires some knowledge of mathematical proofs?