Define spatially varied flow

Spatially varied flow (SVF) is steady, non-uniform open channel flow in which the discharge changes along the length of the channel because water is added or removed along the way, as lateral inflow or outflow. Since $Q$ changes with distance, $dQ/dx\neq0$.

Types

• Increasing discharge (water added along the length): side channel spillway, roadside gutter, drainage channel collecting water from a field, wash-water trough.
• Decreasing discharge (water removed along the length): side weir or lateral spillway, irrigation channel with outlets, bottom rack (trench weir), perforated or porous channel.

 Increasing Q (lateral inflow)      Decreasing Q (side weir)
     |  |  |  |                          ^  ^  ^  (outflow)
 ~~~~~~~~~~~~~~~~~~>  Q grows        ~~~~~~~~~~~~~~~~~~>  Q falls
 ____________________________        _____|side weir|______

The usual momentum or energy equation for gradually varied flow is modified to include the lateral discharge term. In a side channel spillway, for example, the depth changes along the channel as the flow increases.