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Open Channel Flow Gradually Varied Flow Click here to skip to examples.

Key Concepts: Gradually varying flow may occur in sections of the channel as depicted in

the figure below. Start with the basic principles of conservation of mass and conservation of

energy to analyze this type of flow.

Consider varied flow in channels with a rectangular cross section of width, w:

Conservation of mass: w y₁ V₁ = w y₂ V₂ = Q

Conservation of Energy: y₁ + V₁² / 2g = y₂ + V₂² / 2g + ( S_f ˗ So ) L

where y₁ and y₂ are the upstream and downstream depths in ft or in m

V₁ and V₂ are the upstream and downstream fluid speeds in ft/sec or in m/sec

Q is the discharge in ft³/sec or in m³/sec

S_f is the head loss per unit length of channel

So is the channel slope

L is the length along the channel in ft or in m

S_f ≈ [ (k/n) R_H^1/6] ^-2 V² / R_H

Since changes in y and V are gradual, the energy loss can be represented by the

Manning equation and can be used to evaluate the slope for gradually varied flow.

In addition, construct a specific energy plot to aid in evaluation.