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Switching between the normal flow and dynamic flow equation for a conduit is controlled automatically by EXTRAN. The Froude number or the Vedernikov number of the conduit determines the use of the normal flow equation or the dynamic flow equation. Froude numbers > 1.0 (supercritical flow) cause the conduit flow to be calculated from Manning’s equation using the upstream cross-sectional area and hydraulic radius of the conduit. Vedernikov numbers < 1.0 (roll wave formation) also trigger the use of Manning’s equation.


Automatic switching based on the Froude number or Vedernikov number is new to EXTRAN 5. All versions of EXTRAN had automatic switching to the normal flow equation when all of the following three conditions occur in a conduit:

  1. Positive Flow - This criterion is necessary because EXTRAN automatically designates the highest invert elevation as the upstream node and the lowest as the downstream node. This adjustment (if made) is printed out by the model. Positive flow is always from the upstream to the downstream node. Any initial flow entered by the user is multiplied by -1 if the upstream and downstream nodes are changed by the model.
  2. The water surface slope in the conduit is less than the conduit slope.
  3. The flow calculated from Manning’s equation using the upstream cross-sectional area and hydraulic radius is less than the flow calculated by the full dynamic flow equation.

 When all three conditions are met the flow is considered "normal". Normal flow is labeled with an asterisk in the intermediate printout, and the conduit summary lists the number of minutes the normal flow assumption was used for each conduit.

The equation used to calculate the normal flow, Qnorm, is:

Equation 31Image Modified

The Froude number (F#) is calculated as:

Equation 32:  Image Modified


D = the depth of water in the conduit, and the Vedernikov number (V#) for turbulent flow is calculated as:

Image Modified


Rf = Full flow hydraulic radius, and

 Af = Full flow cross sectional area.

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