
69Chapter four: One-dimensional conservation laws
surface is 0.5 m with still water. The ow rate at the upstream boundary is
0.18 m
2
/s and water depth at the outow is set to 0.5 m. Thus, a subcritical
ow condition exists throughout the channel.
=
−− ≤≤
0.2 0.05(10) ,8 12
0, otherwise
2
z
b
(4.63)
0 2 4 6 8 10 12
0
0.1
0.2
Measured
LF
HLL
Roe
Figure 4.12 Comparison of water surface proles for a hydraulic jump.
0 2 4 6 8 10 12
0.1
0.12
0.14
0.16
0.18
q (m
2
/s)
HLL
LF
Roe
Exact
Figure 4.13 Mass conservation in a hydraulic jump.