Find diameter of pipe

Have you looked at the graph of friction factor vs Reynolds number?

 

Yes. You can see that on the chart, the friction factor does not very by several orders of magnitude, at least not for turbulent flow. I would start out with the value at a Re of 10⁵.

 

Like I said, start with the friction factor f for Re = 100000. As far as roughness is concerned, you would have to know that for the particular pipe from its specs or just assume a worst-case value.

 

As I said, the pipe may come with that kind of information when it is purchased. Or, you could choose what you would consider a worst case value. Or, if it a homework problem, they will typically tell you what roughness to use.

 

Once you know D, you will have e/D for the next iteration. So just assume smooth for the first iteration.

 

1. Guess value of D
2. Calculate Re
3. Calculated e/D
4. Determine f
5. Determine h_f and compare with required value
6. Determine difference
7. Go back to step 1
8. Make a graph of either h_f vs D or (h_f difference) vs D.

 

That's what I would do. Choose values for D that give you the exact values of e/D on your Moody chart.