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Apparent shear stress in smooth compound channels

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Abstract

A simple, dimensionally sound, formula is proposed for expressing the apparent shear stress on the vertical interface between main channel and flood plain in a compound channel. An apparent friction factor is introduced and its dependence on the cross-section shape is examined based on experimental results reported in previous studies. For symmetrical smooth channels, it is found that this friction factor is essentially independent of the flow depth and is well linearly correlated with the width ratio of the compound section, at least within the ranges of practical interest where data are available. Discharge estimates obtained by incorporating the predicted shear stress in the ϕ-index method compare well with experimental results. The suggested approach is sufficiently accurate for practical applications and may be extended to other channel shapes and roughnesses depending on the acquisition of adequate data.

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Abbreviations

A m ,A f :

cross-sectional area of main channel and floodplain

b :

width of main channel

B :

total width (of main channel and floodplain)

C fa :

apparent friction factor at the vertical interface bertween main channel and floodplain.

f(·):

function of

g :

accelaration due to gravity

h :

depth of main channel below the floodplain

H :

H=h+y

k :

constant

Q :

total compound section discharge

Q m ,Q f :

discharge in main channel and floodplain sub-sections

Q m′ ,Q f :

respective discharges assuming no interaction

P :

wetted perimeter

R :

hydraulic radius

S 0 :

bed slope

τ :

shear stress

τ a :

average apparent shear stress at the interface between main channel and floodplain

V :

velocity

ΔV :

difference of mean velocity of the main channel and floodplain subsections

w :

specific weight of water

y :

flow depth on the floodplain

γ :

lateral velocity gradient

ρ :

density of water

ϕ m ,ϕ f :

indices accounting for the interaction between main channel and floodplain

f :

floodplain

m :

main channel

References

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Christodoulou, G.C. Apparent shear stress in smooth compound channels. Water Resour Manage 6, 235–247 (1992). https://doi.org/10.1007/BF00872358

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Key words

  • Compound channels
  • flood plains
  • shear stress
  • momentum transfer
  • open channel flow
  • hydraulics