There are three factors affecting the river velocity, this is in term of how fast or slow the river flowing due to the factors of

1. River Gradient

Gradient steep or gentle slope
Steep gradient has fast velocity
Gentle gradient has slow velocity
all of this are due to the force of gravitational force, pulling the speed of the river flowing.

2. Channel Roughness

Smooth or rough channel
Smooth channel has more small pebbles at the bottom of the river bed.( the flow of the river will be faster)
Rough channel has uneven or rough boulders at the bottom of the river bed. ( the flow of the river will be slower)
The smooth and rough channel will determine the friction and this will reduce the velocity of the river.

rough channel

smooth channel

3. The shape of the channel

Shape of the channel also refers to its cross section
The wetted perimeter is the extent to which water is in contact with its channel.
The greater the wetted perimeter , the greater the friction between the water and the banks and the bed of the channel and this will slower the flow of the river. ( the narrow channel will have faster flow of river compared to wider channel will flow slowly )

narrow channel

Wider channel