Friction Factor (f)The friction factor, f, is a dimensionless factor that depends primarily on the velocity u, diameter D, density ρ, and viscosity η. It is also a function of wall roughness which depends on the size ε, spacing ε' and shape of the roughness elements characterized by ε'. Ε and ε' have the dimension of length whereas ε' is dimensionless. Since the friction factor is dimensionless, the quantities that it depends upon should appear in the dimensionless form. In this case, the terms u, D, ρ and η can be rearranged as uDη/η which is the. For the characteristic roughness factors (ε and ε'), it may be made dimensionless by dividing these terms by D (the term ε/D is called the relative roughness).
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