There are several equations that have been developed to describe the friction factor as a function of both the relative roughness and the reynolds number. The equations are dependant on the reynolds number, though. For laminar flow, the equation is simple (f = 16/Re), but turbulent flow, it is much more complex (Colebrook equation, Wood's approximation).
Colebrook Eq: (1/f^0.5)=-4*log[((e/D)/3.7)+(1.255/(Re*f^0.5))]
Wood's Approximation: f = a + b*Re^(-c)
a = 0.0235*(e/D)^(0.225)+ 0.1325*(e/D)
b = 22*(e/D)^(0.44)
c = 1.62*(e/D)^(0.134)
Hope this helps!
jproj