As you know, governing factor for maximum flow that can achieve in any pipe is the available pressure drop. Velocity is just guiding factor to guess optimum diameter of pipe, so as to arrive at right hardware cost (pipe, driver (pump etc)) & right operating cost.
One should also take into consideration erosion in pipe due to high velocity while deciding velocity value.
In your case, available head is about 10 m. If you try to "eat" entire available pressure drop by reducing pipe diameter, you are bound to get high velocity. Hence, suggest you to keep available pressure drop as "reference point" & check that your selected line size shall offer pressure drop below it.
Now your pipe being free flow pipe, you are requested to consider velocity value, that is good for gravity flow (recommended 1 m/s).
Another aspect, that shall be consider is "self venting" requirement. In order to ensure self venting requirement, you need to make sure that froude no. shall be less than 0.3. Accordingly, you need to adjust velocity by changing diameter.
Thus, once you can get all three parameters (recommended velocity, pressure drop, froude no.) matched, you can consider your pipe diameter estimation is correct.
Hope, this answers your query.