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- Created by Unknown User (reynard.juanir), last modified by Abraham Toribio on Jun 22, 2020

The values **V**, **R**, and **A** in equation 18 are weighted averages of the conduit upstream, middle and downstream values at time t and/or t+t. The values at time t+t are the values for the current iteration. At the first iteration they are equal to the previous time step’s values. Adn, Aup, Hdn, and Hup are respectively the conduit cross-sectional area and conduit depths at the upstream (up) and downstream (dn) nodes.**V**·(A/t) is the conduit average area time derivative and conduit average velocity. A is the change in cross-sectional area of the conduit between two time steps.

The basic unknowns in equation 12 and 18 are Qt+t, Hup and Hdn. The variables **V**, **R**, and **A** in turn are all related to the center conduit Q and conduit end values of H. The equation relating the conduit flows to the node H is the continuity equation at a node:

** Equation 21**:

Equations 13 and 21 can be solved iteratively to determine the discharge in each link and the head at each node at the end of a time-step t. The numerical integration of these two equations is accomplished by using an iterative solution using under-relaxation of the linearized momentum and linear continuity equation.

It should be noted that equation 13 has been linearized by:

- Using the product of Qt+t and Qt in the convective inertia term of the dynamic wave equation.
- Using equation 11 for calculating the value of Sf, which does not use the quadratic Q.

- Partial Differential Equations
- Finite Difference Equations
- Implicit Time Weighting
- Significant Differences between EXTRAN Versions 3, 4 and 5
- Finite Difference Solution
- Convergence in EXTRAN
- Automatic Time Step Selection
- Special Conduit Flow Conditions
- Flow and Head Computation during Surcharge and Flooding
- Ground and Invert Elevations
- Flow Control or Diversion Devices
- Storage Devices, Ponds, and Lakes
- Orifices
- Weirs
- Weirs with Tide Gates
- Pump Stations
- Outfall Structures
- Boundary Conditions
- Initial Conditions
- Pit or Junction Losses
- Oscillations during a Hydraulic Jump
- Irregular Closed Conduits
- Irregular Open Channels
- Kinematic and Diffusion Wave Equations
- Special Finite Difference Approximations
- Conduit Depth Calculations