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Steady open channel flows with curved streamlines: the Fawer approach revised

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Abstract

Rapidly varied open channel flows are characterized by curvilinear streamlines, thereby resulting in a pressure field different from the hydrostatic approach proposed in the standard gradually varied flow theory. This problem is related to environmental hydraulic problems such as the undular hydraulic jump and flow over round-crested weirs, for which streamline curvature effects are significant. The inclusion of the curvilinear streamline effect in an extended energy equation was firstly by Fawer. Most of the extended energy equations currently employed are therefore modified forms of the original Fawer approach. The aim of the present study is to highlight and remind engineers of the outstanding theory presented by Fawer. Herein, his approach for steady open channel flow with curved streamlines is revised and compared with experimental observations. Computational methods are presented in detail and based on present results, it can be observed that more recent and complex models for these problems are similar to the original proposal of Fawer, and hardly more accurate in some instances. Based on the proposed study an useful framework for theoretical models for steady open channel flows with curved streamlines is proposed.

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Abbreviations

C d :

Discharge coefficient (–)

F:

Froude number (–)

g :

Acceleration of gravity (m2/s)

H :

Total energy head (m)

h :

Flow depth (m)

h′:

dh/dx(−)

h′:

d2 h/dx 2(m−1)

h o :

Flow depth at approach flow section (m)

h c :

Critical depth (m) = (q 2/g)1/3

K :

Parameter (–)

m :

Discharge coefficient (–)

n :

Parameter (–)

q :

Unit discharge (m2/s)

L :

Wave amplitude (m)

r :

Radius of curvature at channel bed (m)

R :

Radius of curvature at free surface (m)

R z :

Radius of curvature at elevation z (m)

S :

Specific momentum (m2)

S o :

Channel slope (–)

S f :

Friction slope (–)

U :

Depth-averaged velocity (m/s)

V :

Magnitude of velocity vector (m/s)

V s :

Free surface streamline velocity (m/s)

x :

Streamwise coordinate (m)

x o :

Streamwise position of approach flow section (m)

y :

h/ho(−)

z :

Elevation above channel bed (m)

z b :

Elevation of channel bed (m)

z b' :

dz b /dx(−)

z b'' :

d2 z b /dx 2(m−1)

ω :

Wave amplitude (m)

η :

(h o/h c)3(−)

φ :

Free surface angle with horizontal at reference section (°)

φ z :

Angle of inclination of streamline with horizontal at distance z from channel bed (°)

β :

Boussinesq momentum velocity coefficient (−)

Δp z :

Pressure drop (m)

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Authors and Affiliations

  1. Hydraulic Research Scientist, IAS-CSIC, National Research Council, Spain, c/Fernando Colón n°1, 3 izq., 14002, Córdoba, Spain

    Oscar Castro-Orgaz

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  1. Oscar Castro-Orgaz
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Correspondence to Oscar Castro-Orgaz.

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Castro-Orgaz, O. Steady open channel flows with curved streamlines: the Fawer approach revised. Environ Fluid Mech 10, 297–310 (2010). https://doi.org/10.1007/s10652-009-9157-0

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