turbulent regime

Hello and good day, 

I have completed my Master in Mechanical Eng. (GPA 3.58) from the University of Malay (QS Ranking 114), Malaysia. I have published over 18 ISI articles about convective heat transfer, Turbulent flow and Eco-friendly synthesis of nanofluids in high impact factor journals. I aim to focus on any of the following areas:   

 Hi my friends!

I hope everythin's ok! 

As I previously said I'm doing some researches about fully developed turbulent flow inside an annuli.Now I've faced some problems. Does anyone know how can I calculate Darcy friction factor for a fully developed turbulent regime inside an annuli not using colebrook equations and moody diagram? is there any other way?

I'd be really thankful if anyone could help me .

amin3m6666@gmail.com