Finding the k value in a pipe flow question

[Stacyg]

I am trying to do a pipe flow question but I am having trouble understanding how they have calculated the k values.
Example question 1.1 attached & appendix A1 attached.
We have to use appendix A1 to find the k values. I have tried using interpolation to get the k values from the example question but I am not coming up with same numbers.
Any help would be much appreciated.

Stacy

 

[RTW69]

k values are determined experimentally.