Free surface flows 87
S2 and S3 surface profiles. More specifically, some suggested boundary
conditions are
M1 profile: Y d = 1.5y n
M2 profile: Y d = (y n + y c )/2
S2 profile: Y u = (y n + y c )/2
S3 profile: Y u = 0.1y n
where Y d and Y u are the water depths at the downstream and upstream
control section, respectively. The computational step was selected as
Δx = 1 m.
For the case of a trapezoidal channel, the computed critical depth
(y c  = 1.25 m), normal depth (y n = 2.19 m) and the water surface M1
profile are illustrated in Figure 5.3. From that figure it can be easily
seen that the M1 profile extends to approximately 2500 m upstream
from the control section.
Computer code 5.1
% Example 5.1 Water Surface Profiles
% Q = Volumetric discharge [m^3/s];
% S = Bed slope;
% Sf = Energy gradient;
7
6
5
4
3
2
1
0
–4000 –3500 –3000 –2500 –2000 –1500 –1000 –500
0
Elevation (m)
Distance (m)
Bed
Water surface
Critical depth
Normal depth
Figure 5.3 Water surface profile (M1 curve).