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**The Diffusion wave equations** are obtained from the unsteady flow continuity equation and momentum equation by neglecting the local inertia and convective acceleration terms in the momentum equation [Sjosberg, 1981]:

**Equation 51:**

**Equation 52**:

Note

The bottom slope is incorporated into the gradient of H.

An advantage of the diffusion wave equation is the absence of wave characteristics and hence no distinction must be made between subcritical and supercritical flows. The solution will be continuous because a hydraulic jump cannot develop.

The kinematic wave assumption is even simpler than the diffusion wave approximation since the pressure term is also ignored in the solution. The kinematic solution is bed slope equals friction slope, or So = Sf.

EXTRAN uses the Kinematic Wave equation for special flow situations.

- 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