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?