(Bug?) HP48 Equation Library

[Han]

So in the process of creating a data file to replicate the HP48 Equation Library, I noticed that there were possibly bugs in some of the formulas.

In the Advanced User's Guide (for the HP48), Section 4-26 shows a formula that is part of the Flow with Full Pipes system of equations.
\[ \rho \cdot \underbrace{\left(\frac{\pi \cdot D^2}{4}\right) }_\text{Area} \cdot v_\text{avg} \cdot \left( \frac{\Delta P}{\rho} + g \cdot \Delta y + v_\text{avg}^2 \cdot \left( 2 \cdot f \cdot \frac{L}{D} + \frac{\Sigma K}{2} \right) \right) = W \]
The problem is that \( f \) is never defined anywhere. Instead, there is reference to an \( \epsilon \) (roughness) that is defined as a variable, but never used.

I don't know anything about hydraulics, so I have no idea if this formula is correct. But as is, the system cannot solve for all variables (namely \( \epsilon \)). Moreover, many terms may not be solvable because it never sets up the variable \( f \) (because it is not defined for the system). There are a few other systems like this. As another example, Cantilever Moment has the equation
\[ Mx = P \cdot (x-a) + M - \frac{W}{2}\cdot (L^2-2\cdot L \cdot x + x^2) \]
This system defines a variable \( c \) that is never used in this formula. Are there any engineers and/or physicists here who can shed some light on these formulas?