Water Surface Pressure Gradient (WSPG) is a hydraulic analysis model that computes and plots uniform and non-uniform steady flow water surface profiles and pressure gradients in open channels or closed conduits with irregular or regular sections. The Los Angeles County Department of Public Works (LADPW) requires use of this model for hydraulic design. Extensions and modifications to the program have also been made for Alameda County allowing it to conform to their local design standards.


WSPG was originally developed by the Design Systems and Standards Group of the Design Division and the Data Processing Section of the Business and Fiscal Division of the Los Angeles County Flood Control District. This program was originally written as a mainframe program called F0515P for use by the Los Angeles County Flood Control District or by its Contractors on District projects. The program was written in FORTRAN IV, compiled using the IBM FORTRAN H compiler executing on an IBM 370/158 using OS/VS2 MVS. The system required the use of an input media (such as a card reader), temporary disk storage, and a printer. It was designed to run in batch mode.

In the past there have been two implementations of the WSPG: a public domain DOS program, and a menu-driven, non-graphical Windows interface.

In April 2009, the LADPW contracted with XP Solutions (now Innovyze) to update the WSPG hydraulic engine and embed that engine in a graphical user interface, namely the interface for XPSWMM/XPStorm.

In 2011, Alameda County contracted with XP Solutions (now Innovyze) to extend the existing product to allow it to conform to their local design standards. This is referred to as Alameda mode within the software. This Alameda mode is enabled by selecting Alameda mode in the WSPG Job Control.

Purpose of WSPG

The program computes and plots uniform and non-uniform steady flow water surface profiles and pressure gradients in open channels or closed conduits with irregular or regular sections. The flow in a system may alternate between super critical, subcritical or pressure flow in any sequence. The program will also analyze natural river channels although the principle use of the program is intended for determining profiles in improved flood control systems.

The collaborative effort between XP Solutions (now Innovyze) and the LADPW has resulted in WSPG being available.

General Program Description

XP Solutions (now Innovyze) reviewed and updated the original LADPW code for WSPG. Notable modifications are herein indicated. The XP Solutions (now Innovyze) re-write of WSPG primarily converted the FORTRAN to the more current programming code, C++. The capability to handle a branching (dendritic) network was added.

Where applicable, extensions to the program in fulfillment of a contract to localize WSPG to Alameda County design standards are also indicated. Within this help file those dialogs will be shown along with the dialogs in normal WSPG mode. Some of these extensions included the addition of new conduit shapes and drop structures which are available in both modes.

Basic Theory

The computational procedure is based on solving Bernoulli’s equation for the total energy at each section and Manning’s formula for friction loss between the sections in a reach. The open channel flow procedure utilizes the standard step method. Confluences and bridge piers are analyzed using pressure and momentum theory.

The program uses basic mathematical and hydraulic principles to calculate all such data as cross sectional area, wetted perimeter, normal depth, critical depth, pressure and momentum.

The program processes the computations in three phases: Analysis of the system in the downstream direction (Phase I), analysis of the system in the upstream direction (Phase II), and analysis of the downstream profile (from Phase I) and the upstream profile (from Phase II) to obtain a composite profile (Phase III). The processing was designed to continue calculating unless gross errors are encountered. In cases where the downstream or the upstream processing does not yield a HGL solution then the resulting HGL is based on the sole computed value. Warning messages may be issued concerning tolerance levels not being reached on an iterative approximation. These may or may not affect the overall solution to the problem; however, processing continues. If gross errors are encountered, an error message will be issued and processing will stop.

Computational Procedures

Input Preparation

The channel or conduit system is initially subdivided into the following elements: system outlet, reach, transition, confluence (junction), bridge exit, bridge entrance, wall entrance (sudden contraction), wall exit (sudden expansion), join, drop and system headworks. The join and the drop structure are new elements introduced by XP Solutions (now Innovyze) as extensions to previously released versions of WSPG. Each element is internally assigned a number. Additional “intermediate points” between elements are internally set by the program. Stationing is entered by the user only at the System Outlet (SO); the program uses the “length of element” to calculate the stationing.

The entire input is thoroughly scanned for required information and range values of optional information before processing begins. If any errors are detected, processing will stop. Warnings may be issued, but the program will not be prevented. The input data must consist of a minimum of three elements (system outlet, system headwork and other element). The original WSPG program was limited to a maximum of 200 elements. With the XP Solutions (now Innovyze) update to WSPG, that limitation was removed.

Flow Rates

The starting flow rate (Q) at the upstream terminus of a system is specified in the System Head Works (SH) node. The flow rate (Q) is increased at the desired locations by specifying lateral inflow rates in a Junction (JX) node and from branches tied to the main line using a Join (JO) node. The flow rate can be reduced by using a negative lateral branch flow rate in Junction (JX) nodes.

Manning’s “n”

The program uses the Manning formula for the friction loss in all types of conduits or natural channels. The program can only take one “n” value per element; however, the “n” value can change at subsequent elements. If a section has a lining composed of different roughness coefficients a composite “n” based on anticipated depth of flow should be hand computed. If an “n” value is not specified with the input data, the program uses a value of .013.

Suitable values of Manning’s n can be selected from these tables from the United States Department of Transportation – Federal Highway Administration: Hydraulic Engineering website.


Manning's n Values for Closed Conduits.

Description

Manning's n Range

Concrete pipe

0.011–0.013

Corrugated metal pipe or pipe-arch:

Corrugated Metal Pipes and Boxes, Annular or Helical Pipe (Manning's n varies with barrel size)

68 by 13 mm (2-2/3 x 1/2 in.) corrugations

0.022-0.027

150 by 25 mm (6 x 1 in.) corrugations

0.022–0.025

125 by 25 mm (5 x 1in.) corrugations

0.025–0.026

75 by 25 mm (3 x 1 in) corrugations

0.027–0.028

150 by 50 mm (6 x 2 in.) structural plate corrugations

0.033–0.035

230 by 64 mm (9 x 2-1/2 in.) structural plate corrugations

0.033–0.037

Corrugated Metal Pipes Helical Corrugations, Full Circular Flow

68 by 13 mm (2-2/3 x 1/2 in.) corrugations

0.012–0.024

Spiral Rib Metal Pipe

Smooth walls

0.012–0.013

Vitrified clay pipe

0.012–0.014

Cast-iron pipe, uncoated

0.013

Steel pipe

0.009–0.013

Brick

0.014–0.017

Monolithic concrete:

1. Wood forms, rough

0.015–0.017

2. Wood forms, smooth

0.012–0.014

3. Steel forms

0.012–0.013

Cemented rubble masonry walls:

1. Concrete floor and top

0.017–0.022

2. Natural floor

0.019–0.025

Laminated treated wood

0.015–0.017

Vitrified clay liner plates

0.015

Manning's Roughness Coefficients for Various Boundaries.

Rigid Boundary Channels

Manning's n

Very smooth concrete and planed timber

0.011

Smooth concrete

0.012

Ordinary concrete lining

0.013

Wood

0.014

Vitrified clay

0.015

Shot concrete, untroweled, and earth channels in best condition

0.017

Straight unlined earth canals in good condition

0.020

Mountain streams with rocky beds

0.040 -0.050

MINOR STREAMS (top width at flood stage < 30 m)

Streams on Plain

1. Clean, straight, full stage, no rifts or deep pools

0.025–0.033

2. Same as above, but more stones and weeds

0.030–0.040

3. Clean, winding, some pools and shoals

0.033–0.045

4. Same as above, but some weeds and stones

0.035–0.050

5. Same as above, lower stages, more ineffective slopes and sections

0.040–0.055

6. Same as 4, but more stones

0.045–0.060

7. Sluggish reaches, weedy, deep pools

0.050–0.080

8. Very weedy reaches, deep pools, or floodways with heavy stand of timber and underbrush

0.075–0.150

Mountain Streams, no Vegetation in Channel, Banks Usually Steep, Trees and Brush Along Banks Submerged at High Stages

1. Bottom: gavels, cobbles and few boulders

0.030–0.050

2. Bottom: cobbles with large boulders

0.040–0.070

Floodplains

Pasture, No Brush

1. Short Grass

0.025–0.035

2. High Grass

0.030–0.050

Cultivated Areas

1. No Crop

0.020–0.040

2. Mature Row Crops

0.025–0.045

3. Mature Field Crops

0.030–0.050

Brush

1. Scattered brush, heavy weeds

0.035–0.070

2. Light brush and trees in winter

0.035–0.060

3. Light brush and trees in summer

0.040–0.080

4. Medium to dense brush in winter

0.045–0.110

5. Medium to dense brush in summer

0.070–0.160

Trees

1. Dense willows, summer, straight

0.110–0.200

2. Cleared land with tree stumps, no sprouts

0.030–0.050

3. Same as above, but with heavy growth of sprouts

0.050–0.080

4. Heavy stand of timber, a few down trees, little undergrowth, flood stage below branches

0.080–0.120

5. Same as above, but with flood stage reaching branches

0.100–0.160

MAJOR STREAMS (Topwidth at flood stage > 30 m)

The n value is less than that for minor streams of similar description, because banks offer less effective resistance.

Regular section with no boulders or brush

0.025–0.060

Irregular and rough section

0.035–0.100

Alluvial Sand-bed Channels (no vegetation)

Tranquil flow, Fr < 1

Plane bed

0.014–0.020

Ripples

0.018–0.030

Dunes

0.020–0.040

Washed out dunes or transition

0.014–0.025

Plane bed

0.010–0.013

Rapid Flow, Fr > 1

Standing waves

0.010–0.015

Antidunes

0.012–0.020

Overland Flow and Sheet Flow

Smooth asphalt

0.011

Smooth concrete

0.012

Cement rubble surface

0.024

Natural range

0.13

Dense grass

0.24

Bermuda grass

0.41

Light underbrush

0.40

Heavy underbrush

0.80

Starting Water Surface Elevations

Starting water surface elevation at the downstream terminus (System Outlet) or the upstream terminus (System Headworks) are optional input values. If not specified, the program will use critical depth elevation to begin computations.

In a branch connected to a Join (JO) node it has a downstream starting water level from the elevation in the main line at the Join node.

Critical and Normal Depths

Critical depth is computed for every section for the given Q utilizing the “Specific Energy Equation”. Normal depth is computed in every reach element on a positive slope for the specified Q.

Velocity Head

The velocity head (HV) is computed using the mean velocity of the section. This may not be accurate in the case of a complex section such as one with shallow flow in the horizontal overbank area where velocity distribution is not uniform. If the program is to be used in this situation the user should be aware that some error may be introduced in the results.

In cases where the velocity is not uniform the user is encouraged to switch to two-dimensional modeling such as the capability found in XPSWMM/XPStorm with the 2D module.

Water Surface Stages

As previously stated, the program processes in three stages. The lower stage water surface (w.s.) profile begins at the system headworks and ends at the system outlet. The computation will proceed downstream in every consecutive element as long as energy is available to maintain flow in the supercritical stage. When energy becomes expended at any point in an element, the lower stage profile will be discontinued from that point to the downstream end of that element. Then computation will resume in the next element with a critical depth control until the system outlet is analyzed.

The upper stage w.s. profile begins at the system outlet and ends at the headworks. Computation proceeds upstream in every element as long as the water surface at the downstream end of any two adjacent points can support the moving mass of water to flow at the critical or subcritical depth. Otherwise, computation will be discontinued from the downstream point to the upstream end of that element. Then computation will resume at the downstream end of the next element with critical depth control, provided no depth less than critical depth has been computed at that point on the lower stage profile. Then computation will proceed up stream until the system headworks is analyzed.

If the computed depth of flow in any open section exceeds the given section height the program will extend vertical walls; a note is provided in the output file indicating the computed water surface elevation is greater than the ground elevation.

The jump routine begins at the system outlet and ends at the headworks. It searches the lower stage and the upper stage profiles for points of equal energy. If a jump is encountered, it will be approximately located, and data on either the upper stage or lower stage not consistent with the greater energy theory will be deleted from every element. The final profile will be a composite of upper stage and lower stage with hydraulic jumps in between.

Data Processing System Description

Prior to the XP Solutions (now Innovyze) update to the WSPG program, the program was written in FORTRAN IV code, compiled using the IBM FORTRAN H compiler executing on an IBM 370/158 using OS/VS2 MVS. This system required the use of an input media (such as a card reader), temporary disk storage, and a printer. It was designed to run in batch mode. The XP Solutions (now Innovyze) update, intended for use on personal computers, used C++ code, includes a graphical user interface and added the Join and Drop elements, allowing branching (dendritic) networks to be included in a single model.

Data required to build a stream network model is similar to the DOS version of WSPG. Required data is now input through a series of dialogs. These dialogs are easily accessed by double-clicking on links and nodes of the model network. In cases where the forced node-link-node combination of elements does not conform to the WSPG element types a dummy node or link can be selected.

The entire input is thoroughly scanned for required information and range values of optional information before processing begins. If any errors are detected, processing will stop. Warnings may be issued, but they will not prevent processing.

Processing consists of three phases: Analysis of the system in the downstream direction (Phase I), analysis of the system in the upstream direction (Phase II), and analysis of the downstream profile (from Phase I) and the upstream profile (from Phase II) to obtain a composite profile (Phase III). The processing was designed to continue calculating unless gross errors are encountered. Warning messages may be issued concerning tolerance levels not being reached on an iterative approximation. These may or may not affect the overall solution to the problem, however, processing continues. If gross errors are encountered, an error message will be issued and processing will stop.

Output of the system consists of an output file that can be viewed from within the program or externally using a text editor.

Element Types and Construction

The channel, conduit or natural river system to be analyzed is subdivided into elements. The XP Solutions (now Innovyze) version of WSPG represents a change in the order and manner in which a model is constructed. The geographical interface maintains geographical orientation (x,y) of elements. To maintain flow direction, the drainage network is digitized from upstream to downstream.

The following element types are input as Node or Link element data as shown below:

Node Element Data

Boundary Lines

All elements are bounded on the upstream end by Section 1 and the downstream end by Section 2 except System Outlet (SO) and System Headworks (SH) which only have Section 1. The user inputs data such as base width, conduit height, etc. for Section 1 of every element. The data for Section 2 for every element is taken by the program from the upstream Section 1 of the adjacent downstream element. Elements may have considerable length between Section 1 and Section 2 as in a reach element or may have a zero length as in a bridge entrance element.

L = length of element

X= number of the element under consideration

X+1= adjacent upstream element

X-1= adjacent downstream element
 

Bridge Entrance (BE)

A bridge entrance is an element used where flow enters from an element without piers into an element with piers. It is considered to have a zero length element even though the bridge pier nose may have a minor length.

The user should supply the pier area reduction factor. Value must be between 0 and 1. The program uses a default value of 1.0 (See Hydraulic Handbooks for typical values).

Details for this element can be entered in the Bridge Entrance Data Dialog.


Bridge Exit (BX)

The bridge exit is also considered to have a zero length element.

A bridge exit is an element used where flow exits from an element with piers into an element without piers.

  • Element X-1 may be a SO, R, JX, JO or TS.
  • Element X+1 may be a SH, R, JX, JO or TS.

It is noted that neither Section 1 nor 2 can be a pipe.

Data for this element can be entered in the Bridge Exit Element Data Dialog.

Drop (D)

The drop structure element is used where there is a vertical drop along a closed conduit system and head losses are expected. The new node element type is needed to allow for drop structures as defined by Alameda Co. Minor Losses Criteria (see section 7 of Alameda Co. criteria document):

For total energy loss, the Alameda method specifies: Hj = Hj1 + Hb

Where:

Hj1 is the energy loss at the junction (original WSPG code does this)

Hb is the angle loss at the junction

In XPSWMM and XPStormthe Drop Structure element type requires the following variables for input by the user:

    • Invert Elevation (U/S)
    • Ground Elevation
    • Outflow entrance loss coefficient (Ko) – 0.1 default; range is within 0.1 to 0.5

A check is performed that upstream channel and downstream channels are “closed” channel types only (closed pipes would be normal, but it is possible to use this element with closed rectangles, trapezoidal or irregular channels.

The energy loss through the drop structure is computed in accordance with the Minor Losses Criteria (section 7) method. Minor loss is essentially = Ko (V22/2g). The parameters needed for the computations come from the upstream channel and the downstream channel (as with other node type operations).

Note: this new element type is allowed in either regular WSPG or Alameda WSPG mode. Data for the element can be entered in the Drop Structure Data Dialog.

Calculation Processing of Drop Structures

Downstream processing

Input: Flow, depth at incoming conduit of drop structure

We simply do not have the knowledge about a backwater condition at this stage.

Treat the outgoing conduit as a headwork is treated, i.e. restart the computation there with critical downstream depth.

Upstream processing

Input: Flow, flow depth at outgoing conduit, velocity in outgoing conduit

Compute water surface depth/EGL2 = flowdepth + velocity^2/2g + K*+ velocity^2/2g

Treat the incoming conduit as a system outlet is treated, i.e. restart the computation there using MAX(EGL2, critical upstream Depth)

The decision on the profiles in control is as follows:

If the generated water surface elevation in the upstream processing is above the water depth proposed by the downstream processing, the upstream processing is in control at both ends.

Otherwise there will be no backwater effects and whatever profile offers the larger force at each end will be in control. No hydraulic jumps will be reported for drop elements.

Join Structure (JO)

The join structure element is used where there is lateral inflow into the system. Element X-1 can be any other element except a System Headworks (SH). Element X+1 can be any other element except a System Outlet (SO).

Details for this element can be entered in the Join Element Data Dialog. 

Junction Structure (JX)

The junction structure element is used where there is lateral inflow into the system. Two different laterals can be handled by this element. Element X-1 can be any other element except a System Headworks (SH). Element X+1 can be any other element except a System Outlet (SO).

 

Data for this element can be entered through the Junction Element Data Dialog.


System Headworks (SH)

The system headworks is the upstream terminus of a channel. Element X-1 can be any element except a system outlet.

 

The System Headworks is always at the uppermost upstream element of a stream or branch network. The headwork represents the stream’s inflow boundary condition. The flow rate is input as cubic feet per second (cfs). System headwork water surface elevation is in feet. The previous element’s elevation and channel type must be used.

Data for this element is entered through the System Headworks Element Data Dialog.

System Outlet (SO)

The system outlet is the downstream terminus of a channel. X is equal to one. X+1 can be any element except a System Headworks (SH). 

Each WSPG model has exactly one outlet which is the most downstream element. There can be no further downstream elements. The outlet constitutes the outflow boundary condition. The Station is entered on the SO element data dialog. System Outlet Water Surface Elevation is in feet.

Data for this element can be entered through the System Outlet Element dialog.

Wall Entrance (WE)

This element is used when there is a sudden change in the conduit section such as a headwall or an abrupt contraction. This element is considered to have a zero length.

 

The user should supply the loss coefficient kc expressed in terms of the velocity head. The program uses a default value of 0.5 for kc. (See Hydraulic Handbooks for typical values.)

Element X-1 may be a SO, R, JX, JO or TS.

Element X+1 may be a SH, R, JX, JO or TX.

The section for element X+1 cannot have piers, however, it can be an open channel or closed conduit. The section for element X-1 can also be an open channel or closed conduit and it can be with or without piers.

Data for this element is entered through the Wall Entrance Element dialog.

Wall Exit (WX)

This element is used when there is a sudden expansion from a smaller to a larger channel or conduit section. This element is considered to have a zero length.

Element X-1 may be a SO, R, JX, JO or TS.

Element X+1 may be a SH, R, JX, JO or TS.

The section for element X+1 may be an open channel or closed conduit with or without piers. The section for element X-1 may be an open channel or closed conduit, however, it cannot have piers.

Data for this element is entered through the Wall Exit Element Dialog.

Link Element Data

Reach (R)

The reach element is a length of channel, drain or natural river with a constant invert slope, Q, cross section and Manning’s n. A reach may have a straight or curving horizontal alignment, however, a curved reach must coincide with the beginning and end of the curve. The same applies to an angle point in the horizontal alignment; a reach must end or begin at the angle point. 

Channel and Conduit Section Description

Channel types may be either opened or closed, regular or irregular. In open channels (regular rectangular or trapezoidal sections) the super elevation of the water surface is computed and printed for each point in the curve. In pressure flow, bend losses, angle point losses, and manhole losses are computed and add to the friction loss for the reach. Element X+1 can be any element except a system outlet. Element X-1 can be any element except system headworks.

The data can be entered in the Reach Element Data Dialog

 

Transition Structure (TS)

A transition structure is a gradual expansion or contraction from Section 1 to Section 2. The length L may be any positive number. Element X+1 may be any element except a system outlet (SO). Element X-1 may be any element except a system headworks (SH).

 

Data for this element is entered through the Transition Structure Data Element Dialog

Channel and Conduit Section Descriptions

Channels and conduits sections are classified as regular or irregular sections. The regular sections (Channel Types #1 - #4 and #7 - #8) are trapezoidal, rectangular channels, box conduits or circular, elliptical and arch pipes. The irregular sections (Channel Types #5 and #6) can be natural river sections or irregular shaped improved sections with or without a cover. Piers or center walls can be included in any section except a pipe section.

From the element data dialog, click the Channel Group button to select or create a channel group while in WSPG mode. Once a channel group has been highlighted, click Edit to launch the WSPG Channel Type dialog.

Channel Shapes are stored in the Global Database and after being entered are available from a selection dialog at other locations. The use of the Global Database for conduit shapes minimizes data entry.

Regular Channel Type Sections

XPSWMM and XPStorm utilizes the following regular sections:

Trapezoidal Open Top, with or without Piers

Trapezoidal Open Channel Dialog

Number of Piers is optional; however, if greater than 0, then a value for the Average width of piers must be input. If the computed water depth is greater than the input Height value, the program will assume vertical walls extend from the ends of the cross section, indicating depth has exceeded the channel height. If piers are present, it is assumed that piers have infinite height.

Rectangular open top with or without piers.

Rectangular Open Channel Dialog

Number of Piers is optional; however, if greater than 0, then a value for the Average width of piers must be input. If the computed water depth is greater than the input Height value, the program will assume vertical walls extend from the ends of the cross section, indicating depth has exceeded the channel height. If piers are present, it is assumed that piers have infinite height.

Trapezoidal/Rectangular Closed Channel

Trapezoidal/Rectangular Closed Channel Dialog

Number of Piers is optional; however, if greater than 0, then a value for the Average width of piers must be input. If the computed water depth is greater than the input Height value, the program will assume vertical walls extend from the ends of the cross section, indicating depth has exceeded the channel height. If piers are present, it is assumed that piers have infinite height.


Circular Single Cell Pipe

Multiple cells are accommodated with Multiple Barrels.

Circular Pipe Dialog

Circular pipe diameter is input in feet. Number of barrels may be input to simulate multiple conduits in parallel such as a double barrelled culvert using a value of 2. Default number of barrels is 1.

Elliptical Pipe

Elliptical pipe height (h) and width (w) is input in feet. It uses the ellipse equation x2/h2+y2/w2 = 1. Number of barrels may be input to simulate multiple conduits in parallel such as a double barrelled culvert using a value of 2. Default for number of barrels is 1.

Arch Pipe

 

An arched pipe is defined by its height only. This value is input in feet. The width is determined by finding the closest match in the Standard Arch Pipe Sizes. The cross section then uses the following normalized data for the depth vs. width representation:

{ .6272,.8521,.9243,.9645,.9846,.9964, 1.0,.9917,.9811,.9680,.9515,.9314,.9101,.8864,.8592,.8284,.7917,.7527,.7065,.6544,.5953,.5231,.4355,.3195}

 Multiple barrels can be used to describe conduits of the same invert and size in parallel.


Multiple barrels can be defined for all closed conduit types (circular, elliptical, arch). Note that multiple barrel pipes cannot be incident to a wall exit or wall entrance.

Irregular Channel Type Sections

XPSWMM and XPStorm utilizes the following irregular cross-sections: 

  • Irregular open top, with or without piers


  • Irregular covered, with or without piers 

Irregular Channel Type Dialog

Selecting the Irregular Channel tab opens the irregular channel editor dialog.  

Restrictions were introduced on the point sets that characterize the cross section of an irregular channel. For an open irregular channel (type 5) the cross section has to be built by a non-strictly monotonously decreasing segment followed by a non-strictly monotonously increasing segment. This means that if following the cross section counter-clockwise, the x-coordinates have to come in a non-decreasing order and the y-coordinates are separable into a first sequence of non-increasing values and a second sequence of non-decreasing values.

Like in the original code, if the y-coordinates of the first and last point are not identical, the redundant part of the cross section will be truncated.

For an irregular closed channel (type 6) a point set that fulfills the requirements has to be built by four subsequent sequences with

  1. non-decreasing x-coordinates and non-increasing y-coordinates
  2. non-decreasing x-coordinates and non-decreasing y-coordinates
  3. non-increasing x-coordinates and non-decreasing y-coordinates
  4. non-increasing x-coordinates and non-increasing y-coordinates.

Definitions & Restrictions for Irregular Sections

An irregular cross section (facing upstream) is defined by x and y coordinates of points I (x,y) given in a counter clockwise direction, from point i=1 to point i=n (minimum 3 points).

Point i = 1 (x,y) is where

x (1) = x min and if x(2) is also x minimum then

y (1) is greater than y (2)

Limitations

Location of x and y axis. The center of the reference axis (x=o,y=o) must not fall on the perimeter of the cross section.

Flow Line Limitation. A section can have only one low flow channel.

Shape Limitations. A section is allowed one minimum and maximum in the x and y directions. For example between points from x minimum to x maximum the consecutive values of x must be equal or greater. From x maximum to x minimum the consecutive values of x must be equal or smaller. The same holds in the y direction.

Piers. The reference (x,y) axis for piers must be the same as used for the cross section. The “y” values are given from left to right.

Axis Limitation. The center of the reference axis (x=o,y=o) must not fall on the perimeter of the cross section.


Angle Point Loss/Curve Loss Coeffcient

WSPG calculates losses using the following equations depending on the switch for the Alameda mode.

For “sharp bends” the equation in WSPG: Ha= 0.0033 Θ (V2/2g)

Where:
Ha is the head loss due to the angle
Θ is the deflection angle in degrees
V is the velocity
g is the gravitational constant

For “gradual bends” the existing equation in WSPG: Hb = 0.2 (V2/2g) SQRT(Φ/90)

Where:
Hb is the head loss due to the bend
Φ is the angle of curvature in degrees
V is the velocity
g is the gravitational constant

For any bend loss in a pipe, the Alameda WSPG equation is: Hb= Kb (V2/2g)

Where:
Hb is the head loss due to the angle
Kb is the energy loss coefficient due to an angle point bend
V is the velocity
g is the gravitational constant 

Default value for Kb is 0.0, a warning message will be issued if the user specifies a value larger than 1.5. However, program will run with this high value.



Angle Losses at Junction/Join

Junction losses in both the original WSPG and in the Alameda mode are the same. Specifically the change in HGL and the Energy Loss are the same. However, the Alameda method specifies the option for angle losses where the original WSPG does not, and:

For total energy loss, the Alameda method specifies: Hj = Hj1 + Hb

Where:
Hj1 is the energy loss at the junction (same as original WSPG)
Hb is the angle loss at the junction

In this implementation, Hb may be 0 where there is straight-line flow of the mainline upstream to downstream. However, if the main line is deflected at an angle as it passes through the junction then Hb will not be 0 and some loss will occur due to the deflection: Hb = Kb (V12/2g)

Where:
Kb is the angle loss coefficient
V1 is the incoming mainline velocity
g is the gravitational constant

Further, the Alameda mode method imposes upper and lower limits on the total energy loss at a junction

Upper limit: Hj = 0.5 V22/2g + V12/2g

Lower limit: Hj = 0.5 V12/2g + V12/2g

Where:
Hj is the total energy loss at a junction
V1 is the velocity of the incoming (upstream) channel
V2 is the velocity of the outgoing (downstream) channel
g is the gravitational constant

The solution checks and enforces that total energy loss does not exceed limits and if it is exceeding then sets the total loss to the limit and recomputes.


Data Input Descriptions

The user creates link-type elements, reaches, transitions, junctions and joins. Once the link is created, starting at the upstream end of the stream, nodes are automatically inserted at each end of a link. These nodes are set to default to dummy nodes. A dummy node has no effect on the computations. The user can then assign a node-type to these nodes or leave as a dummy node. Each node-type element has one incoming link and one outgoing link, with exception of the System Outlet, System Headwork and a Join. All units are US Customary.

WSPG Job Control

Title allows 3 lines of file description and title information.

The Results radio button indicates the output data presented in the output file created by solving the model.

Report intermediate points in the output file can be toggled on or off.

Enabling Alameda County PWA Mode changes some dialogs and allows other options exclusive to WSPG Alameda mode such as the calculation of bend losses.

Link Element Data Dialog

The Element Data dialog allows selection of element type from a pull down list and allows the user to input data associated with that element. Data input requirements vary based on the element selected and if Alameda mode has been selected. As an example, the second dialog shown is with Alameda mode enabled which removes Angle and Radius fields and adds an Angle Loss Coefficient (K_b) for a reach. For reference, a quick view of the results for the selected element is displayed in the Element Data dialog, after the WSPG model has been solved.

The arrows progress the selection either upstream or downstream in the stream network and an object can be directly selected from the list between the arrows.

Station data can only be input at the System Outlet. The program automatically calculates stations for the remainder of the system based on the length of each subsequent element.

Element data represent the upstream end of the element. Node Invert Elevation is the elevation of the element at the upstream end of the element. Node Ground Elevation is the elevation at which the element is assumed to no longer contain the flow.

Channel Group is used to select the channel type from the Global Database.

Reach Element Data Dialog

The Reach element is a length of channel, drain, or natural river with a constant invert slope, flow rate, cross section and Manning’s n-value. Element data for each Reach must be entered in the Element Data dialog. Link length must be entered in feet. Manning’s “n” values must be entered. The program default is n=0.013.

Angle Point for closed channels is entered in degrees. If an angle point is used it is assumed to occur at the upstream end of the reach element. The maximum recommended angle point is 15 degrees.

Angle of Curvature for closed channels is entered in degrees. If an angle of curvature is input to represent a curve in the horizontal alignment of the reach, it is assumed for the entire length of the reach, from start to end.

Radius of Curvature for open channels is entered in feet and has similar restrictions as the Angle of Curvature.

Direction of curvature based on looking upstream in the system, positive (+) angles turn right and negative (-) angles turn left.

Number of manholes is used for the manhole loss calculations.

When Alameda mode is selected in the Job Control the fields ‘Angle Point’, ‘Angle of Curvature’ and ‘Radius of Curvature’ described above are replaced by the field ‘Angle Loss Coefficient (K_b)’.

Angle Loss Coefficient (K_b) is entered when Alameda mode is selected. Enter the appropriate 'K' value for this loss.

Bridge Entrance Data Dialog

Element X-1 may be a SO, R, JX, JO or TS.

Element X+1 may be an R, JX, JO, TS or SH.

It is noted that neither Section 1 nor 2 can be a pipe.

Bridge Exit Element Data Dialog

The Bridge Exit element is used when a channel transitions from a section with piers into a section without piers.

Drop Structure Data Dialog

A Drop Structure can be selected by choosing ‘Drop’ from the Node Element Type drop-down menu. As for all other elements the invert elevation (at the U/S end), the ground elevation and the channel type have to be selected. For this type of structure an additional entry for Outflow Entrance Loss Coefficient must be made. The invert elevation at the D/S end of the drop automatically comes from the downstream link.

Join Element Data Dialog

 

The Join Element is an extension of the Junction Element. The Join introduces a branch of the main stream. Rather than simply adding in flows from a branch, the system can be included in a single model. The branch system is defined similar to the main stream, with the exception that the downstream most element is a Join, rather than a System Outlet. The branch network must have at least one Reach and a System Headworks.

Joins can be adjacent to more than two link elements. For each Join, the mainstream line must be defined.

The program computes the main streamline first and then the branch. The program uses the water depth in the main streamline (from the composite profile) as an initial water surface elevation in branch network.

In the Alameda mode the Mainline Angle Loss Coefficient (K_b) can also be specified. The default for this loss is 0. Enter an appropriate K value for losses for this type of structure based on in-situ geometry. The implementation and details of this loss are described on the section Angle Losses at Junction/Join.

Junction Element Data Dialog

A Junction element is used to introduce a lateral flow, a side flow entering either a channel or pipe. The lateral invert elevation cannot be less than the downstream invert elevation. The junction cannot be bound by either a System Headworks or a System Outlet.

The lateral branch data must be input as well. This data introduces flow to the model.

In the Alameda mode the Mainline Angle Loss Coefficient (K_b) can also be specified. The default for this loss is 0. Enter an appropriate K value for losses for this type of structure based on in-situ geometry. The implementation and details of this loss are described on the section Angle Losses at Junction/Join.

Lateral Branch Data Dialog

The Junction and Join elements require that a Lateral Branch be defined. The Confluence Angle (degrees) is used to calculate entrance losses. The incoming flow rate must be input (cfs). The invert elevation of the lateral branch cannot be less than the downstream invert.

 

Confluence angle must be between 0 and 90 degrees, either positive (+) or negative (-).

Lateral inflow may be negative. 

System Headworks Element Dialog

The System Headworks is always at the uppermost upstream element of a stream or branch network. The headwork represents the stream’s inflow boundary condition. The flow rate is input as cubic feet per second (cfs). System headwork water surface elevation is in feet. The previous element’s elevation and channel type must be used. 

System Outlet Element Dialog

The System Outlet (SO) node represents the terminus of the stream network. Each WSPG model has exactly one outlet which is the most downstream element. There can be no further downstream elements. The outlet constitutes the outflow boundary condition. The Station is entered on the SO element data dialog. System Outlet Water Surface Elevation is in feet.

Wall Entrance Element Dialog

A Wall Entrance is used to model a sudden channel contraction. The channel upstream of the wall entrance cannot have piers. The entrance loss coefficient, Kc, value must be entered by the user, the default value is 0.5

Wall entrance (contraction) loss = Kc * ABS(HV2-HV1)

Where:
Kc = contraction coefficient (0.5 default –acceptable range 0.1 to 0.5)
HV2 = velocity head downstream
HV1 = velocity head upstream

Note: In the current version of WSPG, the equation is the same but the label in Wall Entrance input dialog changed to “Contraction Loss Coefficient (Kc)” instead of Wall Entrance Loss Coefficient. In addition, the acceptable range for this input is (0.1 to 0.5). A warning message is issued if the value is not in this range but the program will accept values equal to or greater than zero.

Wall Exit Element Dialog

A wall exit is used to model a sudden channel expansion. The channel downstream of the wall exit cannot have piers. In non-Alameda mode a default exit loss value of 1.0 is used for this structure and the loss is calculated as follows: 

Wall exit (expansion) loss = 1.0 * ABS(HV2-HV1)

Where:

1.0 = expansion coefficient (hardwired…)

When using the Alameda mode a Wall Exit Expansion Loss Coefficient (K_e) can be specified as a value other than 1.0, the value used by default.

Wall exit (expansion) loss = Ke * ABS(HV2-HV1)

Where:

Ke = expansion coefficient (default 1.0 – acceptable range 0.2 to 1.0)
HV2 = velocity head downstream
HV1 = velocity head upstream

Note: Default is 1.0; a warning message will be issued if the user-specified value is outside the acceptable range, though the program will use this value for the computation.


Transition Structure Data Element Dialog

A transition is a link element for which the channel type is changing from the upstream to the downstream end. The upstream section is input, the downstream section is retrieved from the downstream element.

Node Element Data

The Node Element data is used to specify the type of node from a pull down list and allows the user to input data associated with that node. Data input requirements vary based on the node selected. For reference, a quick view of the results for the selected element is displayed in the Element Data dialog, after the WSPG model has been solved.

The arrows progress the selection either upstream or downstream in the stream network.

Station data can only be input at the System Outlet node. The program will automatically calculate stations for the remainder of the system based on the length of each subsequent element.

Selection dialog

 

Pipe shapes can be entered and selected using the Select dialog. This dialog provides access to the Global Database where various records can be stored. In the case of WSPG this is limited to Conduit Shapes.

Select – After highlighting a record in the list choose Select to pick the conduit for the preceding dialog and close the Select dialog.

Cancel – makes no change or selection of conduit shape for the preceding dialog.

Edit – After highlighting a record in the list choose Edit to enter the conduit data details such as shape and dimensions.

Clear – Remove the selected choice from the preceding dialog.

Rename - After highlighting a record in the list type a new name in the lower rectangular field and then choose Rename to alter the record name.

Delete – After highlighting a record in the list type choose Delete to remove the record from the list and the Global Database.

Duplicate – After highlighting a record in the list type choose Duplicate to create a new record with the same dependent data as the highlighted record. The new record will have a new name created from the old with .1 appended.

Add – Type a name for the record (up to 20 characters) in the lower rectangular field. The select the Add button to add the record to the Global Database and to the list.  

Alameda County Public Works Agency Minor Losses Criteria

HeadLoss in Pipe with Bend


The equation used is:

HB = KB(V2/2g) 

Where:

HB = Energy loss due to bend in pipe (ft)

KB = Energy loss coefficient due to bend without a manhole on junction

V = Velocity of flow in pipe (ft. /sec.)

Θ = Pipe deflection angle (degrees)

D = Pipe diameter (ft.)

R = Radius of bend curvature (ft.)

 


Manhole Headloss

Terminal Manhole (Htm) – Entrance losses for the most upstream manhole.

Equation: Htm=K(V2/2g)

where:

V = flow velocity in pipe
K = varies from 0.1 for smooth pipe entrance to 0.5 for abrupt pipe entrance. (Brater and King)

Manhole (Hm) with Straight Through Flow – No change in pipe size (D1=D2) and no bed angle (Ѳ=0)

Equation: Hm= 0.05 (V2 /2g)

where:

V = flow velocity of downstream pipe

Contraction Loss (Hc) – No bend angle (Ѳ=0) and V2>V1 or D1>D2:

Equation: Hc= Kc (V22/2g – V12/2g)

where:

Hc = Energy loss due to contraction (ft.)

Kc = Contraction loss coefficient (0.1 for gradual contraction to 0.5 for abrupt contraction)

V1 = upstream/incoming pipe flow velocity (ft./sec.)

 V2 = downstream/exit pipe flow velocity (ft./sec.)

D1 = diameter of pipe upstream

D2 = diameter of pipe downstream

g = gravitational acceleration (32.2 ft./sec2)

Expansion Loss (He) – No bend angle (Ѳ=0) and V1>V2 or D2>D1:

Eq. A5) He= Ke (V12/2g – V22/2g) 

where:

He = Energy loss due to expansion (ft)

Ke = Expansion loss coefficient (0.2 for rounded corner to 1.0 for abrupt entrance)

Bend Losses (Hb)

When: D2=D1, the equation used is: Hb= Kb (V12/2g)

When D2>D1, the equation used is: Hb= Kb (V12/2g) + He

When D2<D1, the equation used is: Hb= Kb (V12/2g) + Hc

where:

Hb = Energy los due to bend (ft)

Kb = Bend loss coefficient (obtained from Modern Sewer Design Graph)

Θ = Incoming pipe deflection angle (degrees)

Bend Angle

Kb, with curve or deflector

Kb, with no special shaping

0

0.02

0.02

15

0.06

0.08

30

0.15

0.21

45

0.29

0.39

60

0.48

0.63

75

0.72

0.93

90

1.02

1.33

Junction Losses

Maximum and minimum energy losses at any junction shall not exceed the following upper and lower limits:

Hj = 0.5V22/2g +V1/2g - Upper Limit

Hj = 0.5V12/2g +V1/2g - Lower Limit

Manhole with Straight Flow Mainline, Ѳ1 = 0

Dy=(Q2V2-Q1V1-Q3V3COSq3)/g(A1+A2) (Change in HGL)

Hj=Dy+V12/2g-V22/2g (Energy Loss at the junction)

Manhole with Incoming Flow Mainline Deflected Upstream, Ѳ1 > 0

HJ = HJ1 + Hb

Hj1=Dy+V12/2g-V22/2g (Energy Loss at the junction)

Hb= Kb (V12/2g) (Energy Loss due to bend)

Drop Structures


Case 1 - Elevation of water surface inside the manhole is higher than the crown of the upstream pipe

 

The upstream energy grade line (EGL1) can be computed using the following equation:

 

Where K varies from 0.1 to 0.5 depending on the entrance conditions of the outflow pipe.


Case 2 - Elevation of water surface inside the manhole is below the crown of the upstream pipe.

 

 (When upstream pipe under pressure, YN1>D1)

(When upstream pipe flowing as open channel)

When upstream pipe flows as open channel but subcritical Y= YC1 & V= VC1 However, if upstream pipe flows supercritical Y= YN1 & V= VN1

Where:

FL1 = Invert elevation of upstream pipe (ft.)

V1 = Velocity of flow in upstream (ft./sec.)

D1 = Diameter of upstream pipe (ft.)

VC1 = Critical velocity of flow in upstream pipe (ft./sec.)

YC1 = Critical depth in of flow in upstream pipe (ft./sec.)

YN1 = Normal depth in upstream pipe (ft.)

V2 = Velocity of flow in downstream pipe (ft./sec.)

VN1 = Normal depth velocity of flow in upstream pipe (ft./sec.)

EGL1 = Energy grade line upstream (ft.)

EGL2 = Energy grade line downstream (ft.)

 

References

Handbook of Hydraulics-Sixth Edition by Brater and King

Modern Sewer Design-Third Edition, 1995 American Iron & Steel Institute

Storm Drain Design City of Los Angeles, Department of Public Works 

Warning messages

WARNING 01: Insufficient lateral characterization for junction/join [x].

WARNING 02: Maximum number of laterals for junction/join [x] reached. Rest of data will be discarded.

WARNING 03: No branches given. Join [x] will be treated as a transition.

WARNING 04: Not all elements are connected to the outlet! Computation will only be performed on objects connected to the outlet.

WARNING 05: Too many parameters given for channel section [x]. Excessive parameters will be ignored.

WARNING 06: Upstream channel and downstream channel are the same for transition [x]. Use a reach instead?

WARNING 07: Node [x] has negative invert elevation.

WARNING 08: Number of manholes given for non-closed link [x].

WARNING 09: Pier factor for bridge entrance [x] not in valid range. Pier factor set to 1.0.

WARNING 10: Wall factor for wall entrance [x] not in valid range. Wall factor set to 0.5.

WARNING 11: Element [x] is not connected to the system outlet.

WARNING 12: Link [x] is not connected to the system outlet.

WARNING 13: Pier factor for bridge entrance [x] is below 0.667.

WARNING 14: Wall factor for wall entrance [x] is not between 0.2 and 0.9.

WARNING 15: Invert elevation of element [x] is not larger than invert elevation of the direct downstream element.

WARNING 16: One of the elevations of junction's [x] laterals is set to the invert elevation of the junction.

WARNING 17: One of the confluence angles of junction's [x] lateral is set to 90 degree.

WARNING 18: Length of junction [x] exceeds 100 feet. This is not recommended.

WARNING 19: Right slope in trapezoidal data of channel [x] set to 1.0.

WARNING 20: Left slope in trapezoidal data of channel [x] set to 1.0.

WARNING 21: A pier elevation in channel [x] is set to 0.0 because it exceeded the channel height.

WARNING 22: Element keyword [x] detected when reading a branch name.

WARNING 23: For junction/join [x] fewer branches have been defined than stated by the branch number. Only the defined branches will be processed.

WARNING 24: For junction [x] there are equally named branches.

WARNING 25: Link type element [x] has different invert elevation than its upstream node.

WARNING 26: (Not used)

WARNING 27: (Not used)

WARNING 28: (Not used)

WARNING 29: Normal depth for reach [x] could not be computed accurately. Value used in processing may be inaccurate.

WARNING 30: Internal error. Trying to compute friction slope for element [x] with a negative wetted area or perimeter. Set friction slope to 0.0.

WARNING 31: (Not used)

WARNING 32: Warning! Known depth equaled normal depth in Bernoulli computation for reach [x].

WARNING 33: Upper and lower limits in Bernoulli computation are the same.

WARNING 34: The target value in the Bernoulli computation is not between the bounds.

WARNING 35: (Not used)

WARNING 36: D/S processing stopped in junction [x] because critical momentum is greater than maximum momentum.

WARNING 36: (Not used)

WARNING 37: (Not used)

WARNING 38: U/S processing stopped in junction [x] because the downstream momentum is less than maximum momentum.

WARNING 39: Internal error during U/S processing of transition [x]. Pressure detected but computed depth is less than maximum flow depth. Processing proceeds with less than pressure flow depth.

WARNING 40: (Not used)

WARNING 41: Steep reach in U/S processing detected in which water depth would drop below critical depth. U/S processing stopped.

WARNING 42: (Not used)

WARNING 43: (Not used)

WARNING 44: Jump location in reach [x] cannot be computed.

WARNING 45: One of the elevations of junction's [x] laterals is less than the U/S elevation.

WARNING 46: Channel of junction [x] defined by an irregular point set.

WARNING 47: Junction [x] has a different channel than its direct downstream element.

WARNING 48: Manning's n for pipe flow of element [x] not in recommended range 0.010 - 0.015.

WARNING 49: Manning's n for open flow of element [x] not in recommended range 0.01 - 0.06.

WARNING 50: Upstream processing: Water depth exceeds maximum open channel width for element [x]. Vertical walls used for processing.

WARNING 51: Unknown keyword [x] encountered in [REPORT] section. Program will run with default option.

WARNING 52: Point given for regular channel [x]. Point will be discarded and program runs with regular channel data.

WARNING 53: Headwork [x] has a higher elevation than its direct downstream node.

Error Messages

Error messages 10, 24, 50 and 53 are currently not used

ERROR 1: Memory allocation error in WSPG engine.

ERROR 2: Given channel for object [x] does not exist.

ERROR 3: Element [x] seems to end a streamline but is not a headwork.

ERROR 4: Node [x] is a headwork and has an upstream node.

ERROR 5: Node [x] is the system outlet and has a downstream node.

ERROR 6: Second system outlet [x] given. (Only one system outlet allowed.)

ERROR 7: Object [x] has more than one downstream element.

ERROR 8: Trying to connect the same element [x] to a join twice.

ERROR 9: Object [x] has more than one upstream element.

ERROR 10: Please use ascending order 1,2,3,... for channel numbers. This identifier is invalid: [x].

ERROR 11: Piers defined for channel [x] but average pier width data is missing.

ERROR 12: Point set [x] requested in channel section not found.

ERROR 13: Invalid number of piers (<0 or >10) for channel section [x].

ERROR 14: Not enough pier elevations given for channel [x].

ERROR 15: Channel cross section is changing at node [x]. Must replace node by a WALL-/ or BRIDGE-type node.

ERROR 16: Upstream and downstream channels change for reach [x]. Replace by a transition?"

ERROR 17: Headwork [x] has a higher elevation than its direct downstream node.

ERROR 18: Flow defined at headwork [x] is non-positive.

ERROR 19: Channel type for channel [x] is irregular! Types have to be between 1 and 6.

ERROR 20: Link [x] has non-positive length.

ERROR 21: Invalid curvature for closed channel [x]. Absolute value of curvature must be between 0 and 180 degrees.

ERROR 22: Invalid angle point for closed channel [x]. Angle point must be between 0 and 15 degrees.

ERROR 23: Manhole number of channel [x] must be between 1 and 10.

ERROR 24: Invalid value for Manning's n for channel [x].

ERROR 25: Bridge element [x] cannot have a pipe as its downstream or upstream element. Either replace bridge element or channel definition.

ERROR 26: Channel types at bridge element [x] do not change.

ERROR 27: Channel cross sections of bridge elements [x] downstream and upstream channel do not match.

ERROR 28: Channel types at wall element [x] do not change.

ERROR 29: Upstream channel of wall entrance [x] contains piers. Use a bridge exit instead?

ERROR 30: Downstream channel of wall exit [x] contains piers. Use a bridge entrance instead?

ERROR 31: Junction [x] has a channel of irregular type.

ERROR 32: Point set for channel [x] exceeds maximum allowed number of 99.

ERROR 33: One or more errors were detected while reading the data file. Please correct the above errors first.

ERROR 34: Too many characters in input line.

ERROR 35: Input data incomplete. Too few items.

ERROR 36: Branch [x] is defined twice.

ERROR 37: Invalid keyword [x] in the data file.

ERROR 38: Duplicate ID name [x].

ERROR 39: Undefined object [x].

ERROR 40: Invalid number [x].

ERROR 41: Channel height of channel [x] is not positive.

ERROR 42: Channel width of channel [x] is not positive.

ERROR 43: Total pier width for channel [x] exceeds the channel width.

ERROR 44: Pier width for channel [x] must be a positive number.

ERROR 45: Irregular point set of channel [x] has less than 3 points.

ERROR 46: Irregular point set of channel [x] does not fulfill monotonous sequence requirements.

ERROR 47: Downstream element of element [x] is of invalid type. Element types do not match.

ERROR 48: Upstream element of element [x] is of invalid type. Element types do not match.

ERROR 49: Cannot find element [x]. Has the element been defined?

ERROR 50: Files share same names.

ERROR 51: Cannot open input file.

ERROR 52: Cannot open output file.

ERROR 53: Cannot open binary results file.

ERROR 54: There are more branches defined for junction/join [x] than stated by the branch number.

ERROR 55: [x] is larger than the maximum allowed branch number.

ERROR 56: Branch name [x] has already been used for the join.

ERROR 57: Branch name [x] given in the [NETWORK] section hasn't been assigned to any join.

ERROR 58: The [NETWORK] section is supposed to start with an outlet. It starts with element [x] which is not an outlet.

ERROR 59: The beginning of a branch is expected to start with a join. Element [x] found which is not a join.

ERROR 60: Flow specified at headwork [x] has not the same value than the flow specified at the corresponding join.

ERROR 61: Missing branch for join [x]. More laterals have been defined than branches were given.

ERROR 62: Outlet already used.

ERROR 63: No headwork expected [x], stream too short branch.

ERROR 64: The branch name [x] hasn't been assigned to the join.

ERROR 65: Error in computation! Negative wetted area computed for channel [x]. Abnormal stop of processing.

ERROR 66: Internal error when computing wetted area. Abnormal stop of processing.

ERROR 67: Error in computation! Negative wetted perimeter computed. Abnormal stop of processing.

ERROR 68: Error in computation! Negative depth computed. Abnormal stop of processing.

ERROR 69: Error in processing: No wall obstruction in wall entrance [x] detected. Abnormal stop of computation.

ERROR 70: Abnormal stop during U/S processing of element [x]. Water elevation too high for maximum channel depth."

ERROR 71: Couldn't solve quadratic equation when determining end of pressure flow in reach [x] during U/S processing.

ERROR 72: Abnormal stop during U/S processing of reach: water depth is too high for reach with non-positive slope.

ERROR 73: There was neither a D/S processing nor an U/S processing for element [x].

ERROR 74: Reading the old WSPG data file format failed.

ERROR 75: Junction/Join [x] has a lateral with invalid internal channel number.

ERROR 76: Junction/Join [x] has a lateral whose invert elevation is less than the D/S invert elevation.

ERROR 77: There were errors when validating the input data. Please correct the above errors first.

ERROR 78: Error when validating [x]. A valid channel description for the direct downstream element could not be found.

ERROR 79: Cannot open error log file.

ERROR 80: No system outlet detected.

ERROR 81: Channel [x] not found.

ERROR 82: Channel ID [x] defined multiple times.

ERROR 83: Error in computation! Pier width exceeds top flow width for channel [x]. (Wetted area set to 0.0.)