annuli

 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 [at] gmail.com