Supercritical Flow

Stormwater Studio has the ability to compute supercritical flow profiles with hydraulic jumps automatically. When the energy equation cannot balance, the software initially assumes critical depth and proceeds to the next upstream Line. When finished with the subcritical profile, it reverses the calculation procedure for any Lines (circular, rectangular or open channels) with critical depth assumed at their upstream ends, i.e. from upstream to downstream, and computes the supercritical profile.

Supercritical flow with hydraulic jump

Hydraulic Jump

The Momentum Principle is used for determining depths and locations of hydraulic jumps. At each step (one tenth of the line length) during supercritical flow calculations, Stormwater Studio computes the momentum and compares it to the momentum developed during the subcritical profile calculations. If the two momentums equal, it is established that a hydraulic jump must occur. There may be occasions when a hydraulic jump does not exist or is submerged.

The condition which must be satisfied if a hydraulic jump is to occur is:

The Momentum, M1, of the subcritical profile must equal the momentum, M2, of the supercritical profile.

Where:

Where:
Q = flow rate
A = cross-sectional area of flow
Y = distance from the water surface to the centroid of A

The location of the jump is the point along the line when M1 = M2 and is reported as the distance from the downstream end of the line.

The length of the jump however is difficult to determine, especially in circular 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 depth. Stormwater Studio assumes 5.

Supercritical Flow in Open Channels

Stormwater studio uses the same methodology described above for Lines that are Open Channels.

Profile of an Open Channel in supercritical flow with hydraulic jump

Be sure to read this in-depth article on water surface profiles for storm sewers.

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