Although there can be issues in doing a good translation of technical material, I think that is not all that is going on here. The equation given for drag, drag = k * A * V^2 is not the standard equation. A translator would not change an equation just because they are not familiar with the material. The standard equation is Drag = 0.5 * density * Cd * A * V^2. Looking at these, we see that k is not equal to Cd. The only way I see this making sense is if the author defined his own term, then modified the standard drag equation to fit his term. Again, the main reason I can see for the author doing so is the rather insulting idea that including the density in the equation would make it too hard for freedivers to understand.

Another example of why this is so inconvenient: The way the author defined shape coefficient means the shape coefficient for fresh water is not the same as the one as for salt water, as they have different densities. But the drag coefficient is the same for both. In fact, you could pose a freediver in a wind tunnel, measure the drag coefficient, and use that same value for water.