Channel Studio will use up to a maximum of 25 trials to compute subcritical water surface profiles. If a solution cannot be found, it assumes critical depth and moves onward to the next section. If the calculation option “Supercritical Profiles” is checked On, then Channel Studio will automatically compute a supercritical profile.
Channel Studio uses the same procedure for computing supercritical profiles as it does for subcritical except that it does not consider losses due to contraction and expansion.
The procedure begins at the most upstream section that was found to be at critical depth, uses that as a known starting elevation, and works downstream. Note that supercritical profiles are not computed through bridge sections. These will be skipped.
Hydraulic Jumps
Hydraulic jumps occur when the water surface passes through critical depth. When this happens, the Energy equation is not considered to be applicable. It cannot account for all of the losses generated by Manning’s equation. Thus a different approach is used involving concepts of momentum.
The Momentum Principle is used for determining depths and locations of hydraulic jumps. The software calculates a supercritical profile in the downstream direction until it reaches a cross section that has both a valid subcritical and a supercritical answer. During these calculations, Channel Studio computes the momentum M1, and compares it to the momentum developed during the subcritical profile calculations, M2.
If M1 > = M2, it is established that a hydraulic jump must occur between these two cross-sections.
Momentum, M1, of the subcritical profile must be greater than or equal to the momentum, M2, of the supercritical profile. Note that M is also known as Specific Force (SF) and is reported as such on the Section Results tab.
Where:
Where:
Q = Flow rate
A = Cross-sectional area of flow
Y = Vertical distance from the water surface to the centroid of A
The location of the jump is somewhere along the channel reach when M1 = M2 and is reported as the distance from the downstream section. If M2 > M1, then the upstream force is stronger than the downstream force and the jump just gets pushed through to the next section.
The length of the jump however is difficult to determine, especially in natural channel sections. There have been many experimental investigations which have yielded results which are contradictory. Many have generalized that the jump length is somewhere between 4 and 6 times the Sequent or subcritical depth. Channel Studio assumes 5.
As mentioned in Basic Working Procedures, hydraulic jump locations can be located more accurately by inserting an interpolated section and rerunning the computations.