Link Depth and Node Depth Relationship in SWMM 5

Note:  The depth in a manhole or node in SWMM 5 can be higher than the depth in the connecting links if the link is surcharged.  Typically the upstream link depth is equal to the upstream node depth (if there is not link offsets) and the downstream link depth is equal to the downstream node depth (if there is no offsets) until the link is surcharged and then thenode surcharge depth algorithm is used in SWMM 5 and point iteration equation is used to calculate the surcharge depth in the node.

The Three Flows in SWMM 5 for a Link

The Three Flows in SWMM 5 for a Link

There are actually three flows computed or used for a link in SWMM 5:

1.    The St. Venant Flow equation flow

2.    The Upstream Normal Flow Manning's equation based on the link roughness, slope, upstream cross sectional area and upstream hydraulic Radius,

3.    The flow actually used in the model which is either the flow computed from St. Venant or Manning's equation

The following three links shows how this works in a real model:

·         Link 8040 almost always uses the St. Venant Equation because it is dominated by backwater and surcharge 

·         Link 8100 almost always uses Manning's equation except at the beginning and end of the simulation, 

·         Link 1600 is an adverse slope link and it mainly uses the St. Venant equation. 

·         Flow = the flow actually used during the simulation 

·         Qdynamic = the flow computed from the St. Venant Equation 

·         QNormUp = Flow based on Manning's equation at the upstream end of the link. 

·         QNormDown = Flow based on Manning's equation at the downstream end of the link.

Link 8100 almost always uses Manning's equation except at the beginning and end of the simulation.  The beginning and end of the simulation is when the non linear terms dominant.

Dual Drainage in SWMM 5

Subject:  Dual Drainage in SWMM 5

The purpose of the Dual Drainage tool in InfoSWMM is to create a major or street drainage network on top of an existing pipe or what is called the minor network in  dualdrainage.  The created major network has a node (sometimes called the inlet node) on top of the existing minor network node connected by two  OUTLET links.  One outlet link takes the flow from the street and  passes it to the minor network node, the second outlet link  takes the surcharged minor network flow and passes it to the major network or street – the direction of flow is important (Figure 1).  The general purpose of the Captured OUTLET is to  use a head or depth equation to separate the street incoming  flow into captured flow and bypass flow

Figure 1.  Dual Drainage in General

Figure 2.  How it looks in SWMM 5 with node, outlet and conduit elements.

Two Pass InfoSewer Solution

Two Pass InfoSewer Solution

🔰The Two-Pass InfoSewer Solution method refines the estimation of flow within sewer networks by employing a dual-stage analysis. Initially, in the first pass, the system calculates the loads at each manhole and subsequently deduces the flow in the connecting links. This initial flow estimation is utilized to determine the preliminary depth-to-diameter ratio (d/D), the values of which you are presently mapping.

🔰Subsequently, the second pass of the solution process takes place. This stage is critical as it accounts for complex hydraulic phenomena, including backwater effects, surcharge conditions, and pressurized flow. It is during this phase that the depth-to-diameter ratio is adjusted, often resulting in an increased d/D value compared to the initial pass. This adjusted d/D is depicted in the Hydraulic Grade Line (HGL) plot.

🔰Utilizing the adjusted d/D from the second pass provides a more accurate indication of pipeline capacity and performance, particularly identifying pipes operating at or above 75% fullness. This metric is essential for effective sewer system management, offering a clearer insight into the potential for overflow and the need for infrastructural intervention.

Adjusted d/D is a better way of finding those pipes that are more than 0.75 full

Nodes in InfoSWMM and H2OMAP SWMM

Nodes in InfoSWMM and H2OMAP SWMM

Or how the invert, rim elevation, crown elevation of the highest connecting link, pressure depth and flooded depth interact during a simulation.

Level (invert of the Node)

Elevation (crown – surcharged if the HGL is above the crown elevation)

Ground (either a depth above invert or a Rim Elevation)

Overflow is either lost, stored, increases the HGL, Inlet Controlled or flows to a 2D mesh depending on the values of Surcharge Depth, Ponded Area, Inlet Options or 2D Options, respectively

Maximum HGL Head Class in InfoSWMM AND H2OMAP SWMM

Maximum HGL Head Class in InfoSWMM AND H2OMAP SWMM

Maximum HGL Head Class in InfoSWMM AND H2OMAP SWMM by dickinsonre Maximum HGL Head Class in InfoSWMM AND H2OMAP SWMM You can find the node flood or surcharge maximum occurrence during a simulation in the Junction Summary Report table in InfoSWMM and H2OMAP SWMM (Figure 1) Empty                                   if the Node Head is below or equal to the Lowest Link Connecting  Elevation Below Link Crown            if the Node Head is below or equal to the Highest Link Connecting Crown Below Maximum Depth   if the Node Head is below or equal to the Node Invert + Full  Depth.  The column Max Surcharge Height above Crown will also tell you how deep the Surcharge in a Node. Surchaged                           if none of the above is true. Figure 1.  Junction Summary Report in InfoSWMM Figure 2.  Maximum Surcharge Height above Crown Definition via Blogger http://www.swmm5.net/2013/08/maximum-hgl-head-class-in-infoswmm-and.html

How are Flooded Time, Surcharged Time and Flooded Volume Calculated in InfoSWMM and H2OMAP SWMM?

How are Flooded Time, Surcharged Time and Flooded Volume Calculated in InfoSWMM and H2OMAP SWMM?

How are Flooded Time, Surcharged Time and Flooded Volume Calculated in InfoSWMM and H2OMAP SWMM? by dickinsonre How are Flooded Time, Surcharged Time and Flooded Volume Calculated in InfoSWMM and H2OMAP SWMM? The time, volume and flooded rate shown in the InfoSWMM and H2OMAP SWMM Report File Node Flooding Summary (Figure 2) are calculated as follows (Figure 1): For All Nodes NOT Outfalls ( this includes Junctions, Storage Nodes, Dividers) If the New Volume is greater than the Full Volume of the or there is Overflow then at each time step the Time Flooded is increased If the New Volume is greater than the Full Volume of the or there is Overflow then at each time step the Volume Flooded is increased by the Overflow *Time Step If the New Volume is greater than the Full Volume of the or there is Overflow AND Surface Ponding is Used then the Ponded Volume is New Volume – Full Volume If the Node Depth Plus the Node Invert Elevation is above the Node Crown Elevation then at each time step the time surcharged is increased.   The InfoSWMM andH2OMAP SWMM Map Display variables should be FLOOD_VOLM for the No Surface Ponding option (Figure 3) and PONDED_VOL if you are using the Global Surface Ponding Option (Figure 4). Figure 1.  Levels of Surcharged and Flooding in SWMM 5. Figure 2.  SWMM 5 Node Flooding Summary or the InfoSWMM and H2OMAP SWMM HTML Report file. Figure 3.  The Map Display of the Node Flooding using the No Surface Ponding Option should use the Map Display Variable FLOOD_VOLM Figure 4.  The Map Display of the Node Flooding using the Surface Ponding Option should use the Map Display Variable PONDED_VOL which shows the Maximum Stored Pond Volume. via Blogger http://www.swmm5.net/2013/08/how-are-flooded-time-surcharged-time.html

How are Flooded Time, Surcharged Time and Flooded Volume Calculated in SWMM 5?

How are Flooded Time, Surcharged Time and Flooded Volume Calculated in SWMM 5?

How are Flooded Time, Surcharged Time and Flooded Volume Calculated in InfoSWMM and H2OMAP SWMM? by dickinsonre How are Flooded Time, Surcharged Time and Flooded Volume Calculated in InfoSWMM and H2OMAP SWMM? The time, volume and flooded rate shown in the InfoSWMM and H2OMAP SWMM Report File Node Flooding Summary (Figure 2) are calculated as follows (Figure 1): For All Nodes NOT Outfalls ( this includes Junctions, Storage Nodes, Dividers) If the New Volume is greater than the Full Volume of the or there is Overflow then at each time step the Time Flooded is increased If the New Volume is greater than the Full Volume of the or there is Overflow then at each time step the Volume Flooded is increased by the Overflow *Time Step If the New Volume is greater than the Full Volume of the or there is Overflow AND Surface Ponding is Used then the Ponded Volume is New Volume – Full Volume If the Node Depth Plus the Node Invert Elevation is above the Node Crown Elevation then at each time step the time surcharged is increased.   The InfoSWMM andH2OMAP SWMM Map Display variables should be FLOOD_VOLM for the No Surface Ponding option (Figure 3) and PONDED_VOL if you are using the Global Surface Ponding Option (Figure 4). Figure 1.  Levels of Surcharged and Flooding in SWMM 5. Figure 2.  SWMM 5 Node Flooding Summary or the InfoSWMM and H2OMAP SWMM HTML Report file. Figure 3.  The Map Display of the Node Flooding using the No Surface Ponding Option should use the Map Display Variable FLOOD_VOLM Figure 4.  The Map Display of the Node Flooding using the Surface Ponding Option should use the Map Display Variable PONDED_VOL which shows the Maximum Stored Pond Volume. via Blogger http://www.swmm5.net/2013/08/how-are-flooded-time-surcharged-time.html

Lambda Calculus and Link Variables in the InfoSWMM, H2OMAP SWMM and SWMM 5 Dynamic Wave Solution

Subject:  Lambda Calculus and Link Variables in the InfoSWMM, H2OMAP SWMM and SWMM 5 Dynamic Wave Solution

Successive under-relaxation for the SWMM 5 Dynamic Wave Solution by dickinsonre Subject:  Successive under-relaxation for the SWMM 5 Dynamic Wave Solution SWMM 5 uses the method of Successive under-relaxation to solve the Node Continuity Equation and the Link Momentum/Continuity Equation for a time step.  The dynamic wave solution in dynwave.c will use up to 8 iterations to reach convergence before moving onto the next time step.  The differences between the link flows and node depths are typically small (in a non pumping system) and normally converge within a few iterations unless you are using too large a time step.  The number of iterations is a minimum of two with the 1st iteration NOT using the under-relaxation parameter omega. The solution method can be term successive approximation, fixed iteration or Picard Iteration, fixed-point combinatory, iterated function and Lambda Calculus. In computer science, iterated functions occur as a special case of recursive functions, which in turn anchor the study of such broad topics as lambda calculus, or narrower ones, such as the denotational semantics  of computer programs (http://en.wikipedia.org/wiki/Iterated_function).  In the SWMM 5 application of this various named iteration process there are three main concepts for starting, iterating and stopping the iteration process during one time step: ·         The 1st guess of the new node depth or link flow is the current link flow (Figure 3) and the new estimated node depths and link flows are used at each iteration to estimate the new time step depth or flow.  For example, in the node depth (H) equation dH/dt = dQ/A the value of dQ or the change in flow and the value of A or Area is updated at each iteration based on the last iteration's value of all node depths and link flows.  ·         A bound or a bracket on each node depth or link flow iteration value is used by averaging the last iteration value with the new iteration value.  This places a boundary on how fast a node depth or link flow can change per iteration – it is always ½ of the change during the iteration (Figure 1).   ·         The Stopping Tolerance (Figure 2) determines how many iterations it takes to reach convergence and move out of the iteration process for this time step to the next time step. Figure 1.  Under relaxation with an omega value of ½ is done on iterations 2 through a possible 8 in SWMM 5. This is not done for iteration 1. Figure 2.  if the change in the Node Depth is less than the stopping tolerance in SWMM 5 the node is considered converged.  The stopping tolerance has a default value of 0.005 feet in SWMM 5.0.022.  Figure 3.  The differences between the link flows and node depths are typically small (in a non pumping system) and normally converge within a few iterations unless you are using too large a time step.  The number of iterations is a minimum of two with the 1stiteration NOT using the under-relaxation parameter omega. via Blogger http://www.swmm5.net/2013/08/successive-under-relaxation-for-swmm-5.html

St. Venant equation – this is the link attribute data used when the St. Venant Equation is used inSWMM 5, H2OMAP SWMM and InfoSWMM.  Simulated Parameters from the upstream, midpoint and downstream sections of the link are used.

Normal Flow Equation – this is the link attribute data used when the Normal Flow Equation is used in H2OMAP SWMM. Only simulated parameters from the upstream end of the link are used if the normal flow equation is used for the time step.  The normal flow equation is used if the flow is supercritical or the water surface slope is less than the bed slope of the link.

Non Linear Term in the Saint Venant Equation of SWMM 5

The flow equation has six components that have to be in balance at each time step:

1. The unsteady flow term or dQ/dt

2. The friction loss term (normally based on Manning's equation except for full force mains),

3. The bed slope term or dz/dx

4. The water surface slope term or dy/dx,

5. The non linear term or d(Q^2/A)/dx and

6. The entrance, exit and other loss terms.

All of these terms have to add up to zero at each time step. If the water surface slope becomes zero or negative then the only way the equation can be balanced is for the flow to decrease. If the spike is due to a change in the downstream head versus the upstream head then typically you will a dip in the flow graph as the water surface slope term becomes flat or negative, followed by a rise in the flow as the upstream head increases versus the downstream head.

You get more than the normal flow based on the head difference because in addition to the head difference you also get a push from the non linear terms or dq3 and dq4 in this graph.

InfoSWMM (d/D v. Surcharge d/D)

Subject:   InfoSWMM (d/D v. Surcharge d/D)

What is the difference between the output variables d/D and Surcharge d/D in InfoSWMM and H2OMap SWMM

The d/D is calculated as link capacity based on the midpoint depth of water in the link or Link depth/ Link Maximum Depth
            Since the depth in the link is restricted to the Maximum Depth the d/D value is always between 0 and 1
The Surcharged d/D is calculated from the end node depths at each end of the link
            The two node depths are averaged and the value of Surcharge d/D is the Average Node Depth / Link Maximum Depth,

The value of Surcharge d/D varies from 0 to a large number depending on the maximum depths of the nodes and the possible surcharge depth of the nodes

The value of d/D is based on the middle of the link and the value of Surcharge d/D is based on the average of the node depths at the end of the link.  They may be and often are different.   However, if you have a Surcharge d/D greater than 1 it will indicate at least one end of the link is surcharged.  A Surcharge d/D may be greater than 1 with a d/D less than 1 due to the ends of the node being surcharged and not surcharged.

·         A Surcharged d/D indicates that at least one end of the link is Full, but
·         A d/D value less than 1 does not preclude that one end may be Surcharged.

InfoSWMM (d/D v. Surcharge d/D) by dickinsonre Subject:   InfoSWMM (d/D v. Surcharge d/D) What is the difference between the output variables d/D and Surcharge d/D in InfoSWMM and H2OMap SWMM The d/D is calculated as link capacity based on the midpoint depth of water in the link or Link depth/ Link Maximum Depth             Since the depth in the link is restricted to the Maximum Depth the d/D value is always between 0 and 1 The Surcharged d/D is calculated from the end node depths at each end of the link             The two node depths are averaged and the value of Surcharge d/D is the Average Node Depth / Link Maximum Depth, The value of Surcharge d/D varies from 0 to a large number depending on the maximum depths of the nodes and the possible surcharge depth of the nodes The value of d/D is based on the middle of the link and the value of Surcharge d/D is based on the average of the node depths at the end of the link.  They may be and often are different.   However, if you have a Surcharge d/D greater than 1 it will indicate at least one end of the link is surcharged.  A Surcharge d/D may be greater than 1 with a d/Dless than 1 due to the ends of the node being surcharged and not surcharged. ·         A Surcharged d/D indicates that at least one end of the link is Full, but ·         A d/D value less than 1 does not preclude that one end may be Surcharged. Figure 1.  Plot of d/D and Surcharged d/D in InfoSWMM. via Blogger http://www.swmm5.net/2013/08/infoswmm-dd-v-surcharge-dd.html

How is the St Venant Equation Solved for in the Dynamic Wave Solution of SWMM 5?

Subject:   How is the St Venant Equation Solved for in the Dynamic Wave Solution of SWMM 5?

How is the St Venant Equation Solved for in the Dynamic Wave Solution of SWMM 5? by dickinsonre Subject:   How is the St Venant Equation Solved for in the Dynamic Wave Solution of SWMM 5? An explanation of the four St. Venant Terms in SWMM 5 and how they change for Gravity Mains and Force Mains. The HGL is the water surface elevation in the upstream and downstream nodes of the link. The HGL for a full link goes from the pipe crown elevation up to the rim elevation of the node + the surcharge depth of the node.  The four terms are: dq2 = Time Step * Awtd * (Head Downstream – Head Upstream) / Link Length or dq2 = Time Step * Awtd * (HGL) / Link Length Qnew = (Qold – dq2 + dq3 + dq4) / ( 1 + dq1) when the force main is full dq3 and dq4 are zero and Qnew = (Qold – dq2) / ( 1 + dq1) The dq4 term in dynamic.c uses the area upstream (a1) and area downstream (a2), the midpoint velocity, the sigma factor (a function of the link Froude number), the link length and the time step or dq4 = Time Step * Velocity * Velocity * (a2 – a1) / Link Length * Sigma the dq3 term in dynamic.c uses the current midpoint area (a function of the midpoint depth), the sigma factor and the midpoint velocity dq3 = 2 * Velocity * ( Amid(current iteration) – Amid (last time step) * Sigma dq1 = Time Step * RoughFactor / Rwtd^1.333 * |Velocity| The weighted area (Awtd) is used in the dq2 term of the St. Venant equation: dq2 = Time Step * Awtd * (Head Downstream – Head Upstream) / Link Length The four terms change at each iteration and time step to determine the new flow (Figure 1) based on the two equations: Denom = 1 + dq1 + dq5 Q = [Qold – dq2 + dq3 + dq4] / Denom If you look at a table of the values you will see that the terms add up to zero when the flow is constant and to delta Q or the change in Q when the flow is NOT constant (Figure 2). Figure 1.  The four terms define the new flow at each iteration in the dynamic wave solution of SWMM5 Figure 2.   The magnitude of the four terms determine the flow at the new iteration and ultimately the new Time Step.  If the flow is constant then the value of the term is constant. via Blogger http://www.swmm5.net/2013/08/how-is-st-venant-equation-solved-for-in.htm