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The friction factor, f, is a dimensionless factor that depends primarily on the velocity u, diameter D, density Ï, and viscosity Î·. It is also a function of wall roughness which depends on the size Îµ, spacing Îµ' and shape of the roughness elements characterized by Îµ''.
Hence, the friction factor can be written in a general form as: (3). From this we see that the friction factor of pipes will be the same of their Reynolds number, roughness patterns, and relative roughness are the same. For a smooth pipe, the roughness term is neglected and the magnitude of the friction factor is determined by fluid Reynolds number alone.