I've come across two forms of the Darcy-Weisbach Equation, and each one seems to yield a different result when I am solving for $Q$ (flow).
$$h_{f}=\frac{\lambda Lv^{2}}{2gD}$$
$$h_{f}=\frac{f LQ^{2}}{3D^{5}}$$
How do these equations differ, and what (if any) is the relationship between $f$ and $\lambda$ ?
I think Wikipedia explains it.
Lambda is also called the Darcy friction factor, and equals 4 times the Fanning friction factor, f. The two equations are equivalent, with the first written in the "pressure loss" form, and the second in the "head loss" form.
The first equation uses the Darcy friction factor $\lambda$. The second one I don't know. You could rewrite the first equation. $$ v=\frac{Q}{A}=\frac{4Q}{\pi D^2}$$ $$ \to h_f=\lambda\frac{8Q^2L}{\pi^2gD^5}$$ If you equate the two $h_f$ and solve for $f$: $$ f=\frac{8\lambda}{3\pi^2g} $$ $f$ might be a different friction coefficient, that holds true in certain hydraulic conditions, as $\pi$, $g$ and a constant factor $\frac{8}{3}$ are included in $f$. But I have no clue, where exactly $\frac{1}{3}$ comes from.
