In an open channel flow (flow ...

In an open channel flow (flow with a free surface) one can use Manning's equation if  the flow can be assumed uniform (water surface slope parallel to the pipe slope, long pipe, no backwater effects...etc.).  If the design condition is such that the pipe is full a full pipe flow equation should be used, which accounts for the head differential between the upstream and downstream sections of the pipe. Maximum allowable velocity through the pipe depend on the pipe materials the pipe is made of. My guess is 3 m/s limit is probably related to a concrete pipe where the velocity should not exceed about 9 to 10 ft/s (in the 3 m/s range). I hope this helps.