Depth to Flow

This category is only available for the hydraulic routing methods: Kinematic, Muskingum-Cunge, Muskingum-Cunge Improved, and MacCormack routing. The methods in this category control how flow is translated into velocity, depth, area, top width and celerity for use in the Routing methods.

None

This method is the default for this category. It will result in an error if it is selected and a run is started.

Manning Trapezoid

This method models the channel geometry as a trapezoid.

Slots Specific to This Method

Bottom Width

Type: Scalar

Units: LENGTH

Description: width of the bottom of the channel

Information:

I/O: Required input

Links: Not linkable

Energy Slope

Type: Scalar

Units: NO UNITS

Description: Slope of the reach from upstream to downstream (vertical/horizontal)

Information: Must be positive

I/O: Required input

Links: Not linkable

Mannings Roughness n

Type: Scalar

Units: NO UNITS

Description: Manning’s roughness n, empirical representation of the roughness of the channel

Information:

I/O: Required input

Links: Not linkable

Side Slope

Type: Scalar

Units: NO UNITS

Description: Slope of the sides of the channel, S:1 (horizontal:vertical)

Information:

I/O: Required input

Links: Not linkable

This method uses Newtons method to find a depth corresponding to a given flow. See any open-channel flow book for the equations relating flow and depth to the rest of the parameters for a trapezoidal channel. This method does not produce any output directly, rather the Routing method sets some output slots based on the results of this method.

Manning Wide Rectangle

This method models the channel as a wide rectangle.

Slots Specific to This Method

Bottom Width

Type: Scalar

Units: LENGTH

Description: width of the bottom of the channel

Information:

I/O: Required input

Links: Not linkable

Energy Slope

Type: Scalar

Units: NO UNITS

Description: Slope of the reach from upstream to downstream (vertical/horizontal)

Information: Must be positive

I/O: Required input

Links: Not linkable

Mannings Roughness n

Type: Scalar

Units: NO UNITS

Description: Manning’s roughness n, empirical representation of the roughness of the channel

Information:

I/O: Required input

Links: Not linkable

Method Details

This is the simplest geometry to model. This method assumes that channel depth is negligible relative to channel width, and thus top width and the wetted perimeter are assumed to be equal to the bottom width. This method does not produce any output directly, rather the Routing method sets some output slots based on the flow parameter values calculated by this method.

If flow is zero, then all flow parameter values are zero. Otherwise the following values are calculated:

First the flow parameters and are set (see, for example, Chow et. al., 1988^{1}, p. 283).

where n is the Manning’s roughness coefficient, P is the wetted perimeter (here equal to the bottom width), and S0 is the energy slope.

where Q is the flow value passed in from the Routing method calling this method.

Power Function

This method models the channel geometry as separate functions relating flow to area, area to depth, and flow to top width. Velocity and celerity are derived from the values of these functions.

Note: The exponential calculations are carried out in RiverWare internal units. Flow is in cms, lengths are in m, areas are in m2, and velocity is in m/s. The values set in the Beta parameter slots, as set by the user, must be consistent with these units.

Slots Specific to This Method

Alpha for Area to Flow

Type: Scalar

Units: NO UNITS

Description: coefficient in area/flow conversion

Information:

I/O: Required input

Links: Not linkable

Alpha for Depth to Area

Type: Scalar

Units: NO UNITS

Description: coefficient in depth/area conversion

Information:

I/O: Required input

Links: Not linkable

Alpha for Top Width to Flow

Type: Scalar

Units: NO UNITS

Description: coefficient in topwidth/flow conversion

Information:

I/O: Required input

Links: Not linkable

Beta for Area to Flow

Type: Scalar

Units: NO UNITS

Description: exponent in area/flow conversion

Information: The value in this slot must correspond to flow in cms and area in m2.

I/O: Required input

Links: Not linkable

Beta for Depth to Area

Type: Scalar

Units: NO UNITS

Description: exponent in depth/area conversion

Information: The value in this slot must correspond to flow in area in m2 and depth in m.

I/O: Required input

Links: Not linkable

Beta for Top Width to Flow

Type: Scalar

Units: NO UNITS

Description: exponent in topwidth/flow conversion

Information: The value in this slot must correspond to flow in cms and TopWidth in m.

I/O: Required input

Links: Not linkable

Method Details

The equations involved in this method are as follows:

All of the calculations are carried out in RiverWare internal units (SI units), and parameter values (with no units) should be set accordingly.

Revised: 01/11/2023