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Steady uniform, non-uniform and spatially varied flow

Short answer

Steady uniform: depth, velocity, discharge constant in time and space; water surface parallel to bed. Ex: long prismatic canal, long flume. Steady non-uniform: discharge constant, depth/velocity vary; GVF (backwater curve), RVF (hydraulic jump). Spatially varied: discharge varies due to lateral flow; ex: side spillway, roadside gutter; side weir, irrigation outlets.

Define steady uniform flow, steady non-uniform flow and spatially varied flow. Give at least two practical examples of each flow.

Steady uniform flow

Flow in which the depth, velocity and discharge do not change with time or with distance. The water surface, energy line and bed are parallel (Sw=Sf=S0S_w=S_f=S_0). Examples:

  1. Flow in a long, straight lined irrigation canal of constant section and slope.
  2. Flow in a long, straight concrete flume or drainage channel of constant section and slope, away from its ends.

Steady non-uniform flow

Flow in which the discharge is constant with time but the depth and velocity change along the length. It is of two kinds: gradually varied (GVF) and rapidly varied (RVF). Examples:

  1. Backwater curve upstream of a dam or weir (GVF).
  2. Flow through a channel with a changing slope or section; drawdown at a free overfall (GVF).
  3. Hydraulic jump below a spillway or sluice gate (RVF).

Spatially varied flow (SVF)

Steady flow in which the discharge changes along the channel because of lateral inflow or outflow. Examples:

  1. Side channel spillway, roadside gutter and drainage ditch receiving rainfall run-off (increasing discharge).
  2. Side weir or lateral intake, irrigation canal with many outlets, trench weir or bottom rack (decreasing discharge).
Flow∂y/∂x\partial y/\partial x∂Q/∂x\partial Q/\partial x
Uniform00
Non-uniform≠0\neq00
Spatially varied≠0\neq0≠0\neq0

✓ Answer checked by Claude Opus 5.5 (high effort)

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