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- distance (x) from an initial point (left or right bank)
- depth (y), and
- depth-correction (y~c~ yc )
The depth-correction y~c~ yc may be introduced to evaluate quickly the effects of changes in the cross-section on geometric and hydraulic parameters.
The actual depth y~a~ ya is computed from:
y~a~ ya = y + y~c~ yc
A plot can be made of the cross-section and for levels at fixed intervals, the following quantities are computed, see also figure:
- surface width, (B)
- wetted perimeter, (P)
- cross-sectional area, (A)
- hydraulic radius, (R): R = A/P
- area.(hydraulic radius)2/3 , (A.R^2R2/3^ 3 )
These parameters may be determined for the whole cross-section or for parts of the cross-section, e.g. main river or flood plain.
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- the water boundary is not considered:
- for the flood plain : P~fp~ Pfp = abc
- for the river : P~r~ Pr = cefg
- the water boundary is treated as a wall:
- for the flood plain : P~fp~ Pfp = abcd
- for the river : P~r~ Pr = dcefg
To account for lateral transport of momentum between river and flood plain the latter option appears to be more realistic. It reduces generally the discharge capacity of the main channel. However, to obtain consistency with hydraulic computations, where generally the first approach is used (e.g. wendy), both options are included.
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- surface width, (B)
- wetted perimeter, (P)
- cross-sectional area, (A)
- hydraulic radius, (R): R = A/P
- area.(hydraulic radius)2/3 , (A.R^2R2/3^ 3 )
- discharge, (Q)
- average velocity, (v): v = Q/A
- K-Manning. (energy slope)1/2 , (K~M~ KM .S^1S1/2^ 2 )
The various quantities can be displayed as a function of stage or discharge. The quantity K~M~ KM .S^1S1/2^ 2 is derived from the Manning equation for steady flow:
Q = K~M~ KM A R^2/3^ S^1/2^ R2/3 S1/2
where:
Q = discharge
K~M~ ~~ KM {} = roughness parameter according to Manning (note: K~M~ KM = 1/n, where n is Manning's-n)
A = cross-sectional area
R = hydraulic radius
S = energy slope.
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For extrapolation purposes it may be assumed that for the river section the quantity K~M~ KM .S^1S1/2^ 2 remains approximately constant at higher stages.
Assuming that the same value for S applies for the entire cross-section the roughness ratio between river and flood plain is the only unknown. hymosrequires the entry of the slope S and the K~M~ KM value for the distinguished n parts in the cross-section. The total discharge is then computed from:
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