12d Solutions Pty Ltd CIVIL AND SURVEYING SOFTWARE

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1 Civil and Surveying Software Version 9 Course Notes CIVIL AND SURVEYING SOFTWARE THE 12D PERSPECTIVE 12d Solutions Pty Limited ACN Phone: +61 (2) Fax: +61 (2) training@12d.com

2 12d Stormwater Course - Dynamic Notes These course notes assume that the trainee has the basic 12d Model skills usually obtained from the 12d Model Training Manual These notes are intended to cover basic Stormwater Design. For more information regarding training courses contact 12d Solutions Training Manager. These notes were prepared by Robert Graham Revised May 2010 Copyright 12d Solutions Pty Limited 2010 These notes may be copied and distributed freely. Disclaimer 12d Model is supplied without any express or implied warranties whatsoever. No warranty of fitness for a particular purpose is offered. No liabilities in respect of engineering details and quantities produced by 12d Model are accepted. Every effort has been taken to ensure that the advice given in these notes and the program 12d Model is correct, however, no warranty is expressed or implied by 12d Solutions.

3 1.0 Dynamic Stormwater Design Starting with a Basic Drainage Network Hydro-Rainfall File with Infiltration Intensity Frequency Duration (IFD) Data Rainfall Temporal Patterns Horton Losses SCS NZ Losses (Initial Abstraction and Curve Numbers) Rational to Dynamic ILSAX2 in the DNE Infiltration Losses Storage Losses Rainfall Runoff Calculations ILSAX SCS NZ Dynamic Hydraulics Flows in and out of the Pits Bypass Section Shapes and Slopes Running Dynamic Drainage Storm Analysis Reviewing Results - plan labels Reviewing Results - graphs Adding Storage Basins Overview Selecting the Basin Location The Outlet Structure and the Basin Link Creating the Basin link Data for the Outlet Control Pipe Adding a Second Outlet Structure (Spillway Weir) Natural Section Shapes Orifice Control on a Pipe Storage Tanks as Basin or Pipe Revised May d Stormwater Course - Dynamic Notes Page 1 of 2

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5 1.0 Dynamic Stormwater Design This manual, the Dynamic Stormwater Design, describes how to use 12d model to calculate catchment hydrographs and perform unsteady flow hydraulic computations on drainage networks. The rainfall runoff and loss methods supported include the time area unit hydrograph (ILSAX) with horton infiltration (from runoff), and the New Zealand SCS hydrology method. The starting point for this manual is a 12d drainage network already constructed with catchment areas assigned, inlet and manhole properties set and vertical grading applied. These tasks are described in detail in the Stormwater Part 1 Design Course.:The network will have open channels, bypass flow routes and pits with inlet capacity settings as described in Stormwater Part 2Design Course This manual, Dynamic Stormwater Design Course contains: s s s s s s s s s s review and modifying the 12d hydro file with respect to IFD data, rainfall temporal patterns, infiltration loss methods (horton and SCS curve numbers), selecting the hydrological runoff method (Ilsax2 or NZ SCS) and the infiltration loss method, using cross section shapes cut from the tin for bypass flow paths and open channels running the analysis and reviewing the graphical output, plan and long section plots and the custom spreadsheet reports. create parallel pipes with different sizes and invert levels, adding and initial sizing of storage basin with fixed discharge, discuss graphical basin links, create outlet structures including, culverts, weir spillways, orifice controls, bubble up pits, underground storage tanks, bypass over road crown s 2.0 Starting with a Basic Drainage Network In this document, the generic terms pit or manhole refer to inlets, catch basins and manholes. The exception to this is when referring to inlet types in the Drainage Network Editor (DNE). The term manhole specifically refers to an inlet with zero inlet capacity. Pit types, dimensions and inlet capacities are set in the drainage.4d file. These course notes assume that you have completed the Stormwater Design Course and that you have experience creating 12d model drainage networks with catchments areas. This course will begin with a completed drainage design found in the directory \12d\9.00\Courses\drainage\basins The project name is basins. Revised May d Stormwater Course - Dynamic Notes: Page 3 of 33

6 3.0 Hydro-Rainfall File with Infiltration Access the rainfall editor from the main menu Design->Drainage-Sewer->Rainfall Editor Key Points 1. Several rainfall files are shipped in the 12d library as examples. 2. One of the 3 Intensity method MUST be entered. Do not leave blank rows in the IFD Table. 3. All dynamic drainage runs require temporal patterns. 4. Dynamic drainage (ILSAX 2) requires horton losses 5. Dynamic drainage (NZ SCS) requires SCS losses 6. Rainfall data is in mm/hr NOT mm (important for NZ) 7. Tailwater series are time versus elevation data for outlets. 8. Initial and continuing losses are not supported in release V9c1e 3.1 Intensity Frequency Duration (IFD) Data The IFD table method is the most common (refer to figure above). The rainfall intensity is entered in mm/hr for metric data and in/hr for US units. The top row is the return period in years and the first column is the rainfall duration in minutes. The top left corner cell is always zero. When using the TP 108 method for the Auckland region, the 24hr rainfall depth is extracted from the Appendix A and then converted to mm/hr before entering it into the IFD table. Thus only 2 lines may exist in the 12d grid. Note that areal reduction factors must be accounted for by the user as they are not included in the 12d rational hydrology engine. 12d Stormwater Course - Dynamic Notes: Page 4 of 33 Revised May 2010

7 3.2 Rainfall Temporal Patterns Temporal patterns are referred to as storms in dynamic drainage. Several example hydro files are included in the 12d library. These examples have the temporal patterns for the minor and major storms in the 8 zones of Australia. Temporal patterns are not required for the SCS NZ method as the standard 24 hour temporal pattern from TP108 is built into the 12d analysis engine. The Run storm, Zone filter, From ARI and To ARI columns are used determine which storms are analysed (run). The Run storm column must be checked for that temporal pattern to be analsyed. Many storms may be selected. The Zone filter is optional. Entering a value here will allow the selected storms to be further filterd. A Zone filter field (accepts wild card characters) is found on the DNE Global tab that is used to determine which of the selected storms (paragraph above) are analysed. The ARI field on the Run panel is used with the From ARI and To ARI columns. The value on the run panel must be within the From-To range for the storm to be analysed. The Duration column determines the total length of the storm. This value divided by the Interval must be a whole number and this number determines the number of % values to be entered to the right of the Interval column. The total of the percentage must equal Horton Losses The pervious portion of the catchments used in the ILSAX 2 analysis will have a loss type defined describing the soil type. The loss type is defined in the DNE Default->catchment and catchment tabs. Revised May d Stormwater Course - Dynamic Notes: Page 5 of 33

8 These soil types use the classifications of Terstriep and Stall (1974), based on the system developed by the U.S. Department of Agriculture. The default values entered from the library represent the soil types of 1.Type A - low runoff potential, high infiltration rates (consists of sand and gravel 2.Type B - moderate infiltration rates and moderately well-drained 3.Type C - slow infiltration rates (may have layers that impede downward movement of water) 4.Type D - high runoff potential, very slow infiltration rates (consists of clays with a permanent high water table and a high swelling potential) Numbers are assigned to each soil type to allow interpolation between the defined soil types. When interpolated values are used they must be included in the list (2.5 and 3.5 for example). Interpolated values do not need loss data entered. If loss data is entered for the interpolated names then this data will be used rather than an interpolation occurring. If any loss data is entered then all of the values must be entered. Four preset AMC points are defined in the rainfall file to mark AMC conditions ranging from dry (AMC1) to saturated (AMC4). The required data for each line is the Initial loss rate, Final loss rate, decay rate and 4 antecedent moisture conditions (AMCs). The AMC values are entered in depth of rainfall (mm) they represent the total rainfall prior to the start of the temporal pattern. The AMC point numbers are set once for all catchments on the DNE Global tab. Value between 1 and 4 (decimal value are permitted) are entered for the minor and major events. 3.4 SCS NZ Losses (Initial Abstraction and Curve Numbers) The SCS NZ method uses Initial abstraction (Ia) and the curve number (CN) to determine the losses for the catchments. Names are given to the SCS curve numbers in the rainfall file. These names and Ia (entered as storage values) and selected in the DNE catchment data. A curve number of 0 results in zero runoff while a CN=100 results in 100% runoff. TP 108 recommends the selection of the curve number by identifying 1) the soil type and 2) the land use. A CN=98 an Ia=0 are recommended for impervious areas. 12d Stormwater Course - Dynamic Notes: Page 6 of 33 Revised May 2010

9 4.0 Rational to Dynamic ILSAX2 in the DNE The user does not have to start with the rational hydrology method but since this method has a pipe sizing algorithm it is often run first. The following steps will prepare a drainage network for dynamic hydrology. Changing to ILSAX 2 is done on the DNE Global->Main tab. 4.1 Infiltration Losses If this is the first time in this project you have switched to ILSAX2 you will be prompted for the default infiltration loss. These loss types are retrieved from the rainfall location file (Horton losses) specified above. Select one of these and then select Update All. These losses are only applied to the previous percentage of the catchment. Revised May d Stormwater Course - Dynamic Notes: Page 7 of 33

10 4.2 Storage Losses Both the impervious and pervious portions of the catchments have storage losses. This amount of rainfall depth (in mm) is removed from the start of the rainfall pattern. The default values are entered on the Defaults Catchments Tab. 12d Stormwater Course - Dynamic Notes: Page 8 of 33 Revised May 2010

11 5.0 Rainfall Runoff Calculations 5.1 ILSAX 2 The ILSAX mode 2 uses a triangular shaped unit hydrograph with the time to peak equal to the recession time. The time to peak equals the tc value throughout the 12d DNE. 5.2 SCS NZ The SCS NZ uses a unit hydrograph as described in TP 108 Table 4.1 (hydrograph number of 3/ 4). 12d calculates the time to peak value (tp) = 2/3 the time of concentration (tc). One of the optional tc methods uses the equation derived from a regression analysis of Auckland catchments (BCHF, 1999c). On the Defaults->Catchments->Set 1 tab set the Impervious and Pervious Tc methods to NZ Auckland TP108. The default length and slope values will be used unless they are specified for each catchment. Revised May d Stormwater Course - Dynamic Notes: Page 9 of 33

12 6.0 Dynamic Hydraulics As with the rational method hgl calculations it is essential that the pit grate levels are entered correctly. With no bypass specified, water is lost from the analysis when the hgl exceeds the grate level. When bypass is specified the water will not be lost until the level exceeds the highest bank of the bypass section shape (see below). 12d uses the St Venant unsteady flow and continuity equations to solve for the flows in the pipe network. With these equations it is the water level in the pits that determines how much flow travels through the conduits. The hgl is not calculated from the flows. Viewing the results from this perspective will help immensely. 12d Stormwater Course - Dynamic Notes: Page 10 of 33 Revised May 2010

13 6.1 Flows in and out of the Pits The diagram below shows the possible flows through a pit. When bypass is used, there are 2 hgl levels; one level for all of the conduits with inverts at or above the grate level and another for conduits with inverts below the grate level. The pit inlet capacity and choke factors determine the amount of approach flow that is captured. If the HGL of the subsurface reaches the grate level, the captured flow becomes zero and only the surface hgl is used to determine the flows in all conduits. When the hgl drops below the grate again, 2 hgl levels will again be used. The continuity balance is monitored during analysis and the results of this check are stored as a model attribute dynamic/xx/calculated hydraulic continuity error percent where xx is the duration of the storm. A detailed output file is also created for each storm analysed. The file name begins with the name of the drainage model and ends with the storm duration (plus the extension rpt). Revised May d Stormwater Course - Dynamic Notes: Page 11 of 33

14 6.2 Bypass Section Shapes and Slopes In the rational method, bypass flows (water that could not enter the inlet because of either inlet constrictions or hgl levels) were bypassed to the Bypass pit. With the dynamic analysis, a channel shape is required so that the hgl levels and the storage effects can be modelled. If all of the bypass routes have the same shape then you need only cut one default shape and it will be used for all routes. However you can enter a shape string for every bypass route if desired. The invert elevations of the bypass channel are set by the grate elevation of the upstream and downstream pits. The upstream invert level of the outgoing bypass channel can be manually changed by setting the real pit attribute bypass invert level in versions prior to V9c1f. This is often done to set an overflow level for water passing over the crown of the road. If the bypass is to the pit LOST then the slope of the bypass channel will be 1%. These value can be changed via integer pit attribute bypass grade or the integer model attribute default bypass grade in versions prior to V9c1f. The length is determined from the length of the bypass flow string giving the channel a constant grade. If a changing grade or channel shape is required then the bypass should be to a drainage line modelled as a natural channel (see section further in the notes). The channel shapes are created by drawing a string perpendicular to the flow path and 12d will cut section from the finished surface tin. It is recommended that you keep you section shape strings in one model for data management purposes. The strings are drawn from left to right looking in the direction the bypass string (the direction of flow). To create this string enter the new model name in the CAD Control Bar. Entering a name for the string is optional. If only 2 points are to be used for the shape string then use the Create Line button from the CAD tool bar. 12d Stormwater Course - Dynamic Notes: Page 12 of 33 Revised May 2010

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16 We will now explicitly define a bypass flow shape for anther bypass link. Create a shape string for the bypass across road 2. Draw the string from east to west (left to right looking in the direction of flow). Now select the bypass shape for crossing the crown of the road. The bypass pit and Distance fields will already be completed from the bypass flow string calculations. Entering a manning s n value is 12d Stormwater Course - Dynamic Notes: Page 14 of 33 Revised May 2010

17 optional. If this was to be modelled now the bypass channel would go from one grate level to the other without any reference to the crown of the road level. To model the flow path from the crown of the road to the pit 3.5S we will raise the upstream invert level to the road crest level (25.790). Pre 12d V9c1f you will need to create a real pit attribute bypass invert level. Strings->Properties->Attributes Revised May d Stormwater Course - Dynamic Notes: Page 15 of 33

18 7.0 Running Dynamic Drainage In V9c1e the dynamic engine analyses the network but does not design the components. Multiple storm patterns may be run simultaneously and the results from individual storms as well as the worst case from all currently analysed storms is saved. The results may be viewed graphically or in user defined reports. If your computer has a multiple core processor each storm will be processed by different processors and 12d will accumulate the results as the storms finish analysing. 7.1 Storm Analysis Select the Storm Analysis button. To generate plan labels for the worst case dynamic results select the drainage_dynamic_design ppf file from the library. Also change the name of the Model for plan results so that you can keep the results from previous rational hydrology runs. Select the Run button. 12d Stormwater Course - Dynamic Notes: Page 16 of 33 Revised May 2010

19 A process window will be launched for each storm analysed and the status will be printed in the output window. Always watch this window for messages. Below are message from a sample run, ==> Checking Storm: 1 ==> Storm: 1 OK ==> Updating Catchment Attributes ==> Updating Node Attributes ==> Updating Link Attributes ==> Updating Model Attributes Elapsed Time: 6.67 secs Run finished normally. A run with errors would have a message like the following: Dynamic Drainage Analysis (Build ) Dynamic Runoff Method: ILSAX 2 ari: 10.0 zone: 0 1 TP_Durations: ==> Solving Storm: 1 ERROR: Bypass section not defined for conduit: 7/A-SEP_to_6/A-SEP(S) Model failed to solve. 7.2 Reviewing Results - plan labels As with the rational method, the plan plots indicate the peak values. If multiple storms are run then this ppf file will print the max from all storms run. So that the dynamic results are not mixed with the rational results, the worst case results are stored with the prefix dynamic. Results from individual storms have the prefix dynamic/xx where xx is the max time of the rainfall event. For example the pipe attribute for the maximum pipe flow calculated pipe max flow dynamic/calculated pipe max flow dynamic/calculated pipe max flow critical storm dynamic/25/calculated pipe max flow dynamic/calculated pipe max flow rational hydrology result worst case dynamic result storm where above results occurred 25 min storm dynamic result worst case dynamic result Revised May d Stormwater Course - Dynamic Notes: Page 17 of 33

20 7.3 Reviewing Results - graphs Graphs indicating the results are created on the Graphs tab of the DNE. These graphs are a sampling of the time step results and usually does not include all time steps. Therefore, if the peak indicated in the attributes occurs between 2 plot points the peak may not be on the graph. Select the Storm event to view. Nothing is displayed yet. Now select the data to view using the drop down boxes or by selecting the below and pressing enter. For example the Rainfall/Runoff. 12d Stormwater Course - Dynamic Notes: Page 18 of 33 Revised May 2010

21 The panel cannot be resized but it can be maximised via the right mouse menu. ESC returns to smaller view. The peak from the plot data (not the attribute) is indicated at the top of the graph. You can zoom into the graph areas by dragging a rectangle inside the graph area. You must right mouse select and choose Undo Zoom to return to the full plot. The available graphs are: Catchment graph types (used in conjunction with Sub catchment selection) Rainfall/runoffThe Total rainfall is the storm data merging the IFD data, the return period and the temporal patterns. Excess rainfall (ILSAX 2) is the water that is left over after the rainfall losses infiltrate into the soil. For the impervious area, excess rainfall = total rainfall For the pervious area, excess rainfall = total rainfall - infiltration Runoff starts when the excess rainfall depth exceeds the storage depth. Most frequently runoff starts from the impervious area first, (no infiltration, small storage and short tc) and then from the pervious area. Runoff The runoff component of the Rainfall/runoff graph. Rainfall The rainfall component of the Rainfall/runoff graph. Losses These are the horton infiltration losses that are subtracted from the pervious component of the catchment. Revised May d Stormwater Course - Dynamic Notes: Page 19 of 33

22 Pit graph types 12d analysis has 2 systems for conveying flow. The bypass system created with bypass flow strings (open channels with their inverts at the pit grate levels) and the link system created with the 12d drainage strings. Grate & Invert Depths 2 charts, the top is the Grate depth showing the depth of flow in the bypass channel measured from the grate level. The bottom is the Invert depth showing the depth in the link system above the pit invert. Grate & Invert Elevations 1 chart showing both the bypass and link system water elevations. All Inflows & Outflows Catchment flow is the total flow from all 3 catchment sets, Approach flow is the sum of the catchment flow and incoming bypass flow, Captured flow is the portion of the approach flow that drops down into the link system. It is determined from the inlet capacity rating curves. Bypass flow is the difference between the approach flow and the captured flow. Inflow to invert is the total of all the incoming links system flows plus the captured flow from the bypass system. Outflow from invert is the total of all the outgoing link system flows. Depth above Invert see invert depth above Depth above Grate see grate depth above Elevation - see Invert elevation above Elevation Bypass Flow - see Grate elevation above Basin volume - only available on pits with basin curve data. Catchment Flow - see Catchment flow above Link Inflow + Captured flow - This is the sum of Inflow to invert (see above) + Captured flow which represents the total inflow into the link system pit. Link Outflow - the total outflow from the links (not the bypass) Approach Flow - see above Bypass flow - see above Inflow - Overflow - the flow that exceeds the maximum level at the pit. This flow is lost from the drainage system. The maximum level is the max of the cover level and the (grate level + depth of bypass channel). Ku - the link flow, velocity, Ku and head loss of the outgoing link. 12d Stormwater Course - Dynamic Notes: Page 20 of 33 Revised May 2010

23 Pipe graph types (link system) All Link Results 3 charts HGL US, HGL DS (left axis) Depth (right axis) depth at the mid point of the link Capacity (left axis) the ratio of the current pipe flow / (pipe full, HGL at grade capacity) Froude Number (right axis) - Froude number at the mid point of the link Flow (left axis) flow in the link Velocity (right axis) - velocity at the mid point of the link Bypass graph types (bypass system) same results graphs as for the pipe graph types above Revised May d Stormwater Course - Dynamic Notes: Page 21 of 33

24 8.0 Adding Storage Basins 8.1 Overview The basic components of a storage basin are the basin pit (defined by selecting a basin string or entering elev-area curve data), the basin link (the graphical link joining the basin pit to the outlet structure) and the outlet structure 8.2 Selecting the Basin Location The node modelling the basin is the outlet of the pipe or channel discharging into the basin. The pit becomes a basin when the user enters elevation versus area curve for the basin or selects a polygon around the top of the basin. With the polygon method, 12d will create the elevation versus area curve from the finished surface tin. We will use an existing string from the survey data but you may easily create your own polygon around the top of the basin. For an initial sizing you only need to enter the basin invert elevation and area into the grid. 12d Stormwater Course - Dynamic Notes: Page 22 of 33 Revised May 2010

25 8.3 The Outlet Structure and the Basin Link The basin outlet generally includes more than one structure. Typical arrangements include a low flow pipe that restricts the outflow from the basin and a high flow spillway used in larger events. Every outlet structure is linked to the basin pit with a basin link. Often the outlet structure is a fair distance from the basin pit and we want the outlet structures drawn in their correct location. IF the diameter of the basin link is set to zero it joins the basin pit to the outlet structure but preforms no hydraulic function in the model. The minimum elevation in the elevation data becomes bottom of the basin and the outlet inverts cannot be below this level. If there is a drop pit for the outlet then ensure that the base of the drop pit is first elevation in the basin data. The area will be the area of the pit. The second entry will be the top of pit level with the same pit area. 8.4 Creating the Basin link The pipe downstream of a basin pit is a basin link. When the diameter is set to zero, the data set on this link is for graphical presentation and has no hydraulic function. Revised May d Stormwater Course - Dynamic Notes: Page 23 of 33

26 For clarity in the section view we will set the levels to the bottom elevation of the basin and set a zero pipe diameter to make the link as unobtrusive as possible. Note the Type is locked to Basin. Locking the link inverts will ensure the invert elevations are not changed with a regrade pipe selection. Remember this is a graphical link and the values do not affect the hydraulic calculations. 12d Stormwater Course - Dynamic Notes: Page 24 of 33 Revised May 2010

27 8.5 Data for the Outlet Control Pipe The upstream invert is being set to the bottom of the basin and then we will lock this invert. We will leave the engine to set the DS invert level. The length will depend of your drawing. For initial sizing of the basin you can set the diameter of the pipe to 0.001m so that no flow goes through it. Now enter a negative pipe direct flow and this will become the constant outflow from the basin (usually set to your pre-development peak discharge). Once you size the basin return here, remove the negative flow and select a pipe size to yield similar results. Revised May d Stormwater Course - Dynamic Notes: Page 25 of 33

28 8.6 Adding a Second Outlet Structure (Spillway Weir) A second drainage string will be needed for the spillway. Again it will start with a basin link and then have a weir section. From the main menu select Design->Drainage-Sewer->Create Select the Same as button and pick a drainage string in the model. This will fill in all of fields. Name must be unique so change this data. Finally select Create. Then select Add/Append MH from the menu. 12d Stormwater Course - Dynamic Notes: Page 26 of 33 Revised May 2010

29 The plan view below shows the basin link and the spillway weir location. Draw the string in the direction of flow and ensure you start with a point snap on end of the channel. Once the string has been created the pit data at the upstream side of the weir need to be set. On the Pit->Main tab we are going to set the cover level at the highest expected water level in the basin. The grate level will have the same level as the cover level. The Pit type does not affect the calculations for the weir. We have also assigned a name to this pit. Revised May d Stormwater Course - Dynamic Notes: Page 27 of 33

30 On the pipe-main tab we will see the US invert level to weir crest level (20.0). The DS Invert is set the same but will have no affect on the calculations. The Diam/Height determines when the weir will start acting as an orifice. Generally used in underground storage tanks. In this case we will set is to a value higher than the expect flow depth (1.0 m). The Width is the dimension of the weir perpendicular to the flow. The Disch Coef is optional as the default will be used if it is blank. 12d Stormwater Course - Dynamic Notes: Page 28 of 33 Revised May 2010

31 The tailwater levels are now set to the expected levels for the minor and major events. Enter a name for the outlet. Revised May d Stormwater Course - Dynamic Notes: Page 29 of 33

32 9.0 Natural Section Shapes The channel shape may be cut from the design tin by drawing a string at the desired location. It is a standard convention to draw it from left to right looking in the direction of flow. Enter the model name drainage natural shapes into the CAD toolbar model field before drawing this string. Once you have drawn the string you can select it from the Pipe->Main tab 12d Stormwater Course - Dynamic Notes: Page 30 of 33 Revised May 2010

33 10.0 Orifice Control on a Pipe Use the Strings->Points Edit->Insert command to add a pit upstream of the outlet pipe. This new pipe will be set to an orifice to control the flow entering the pipe. Lock the invert levels so that the orifice will not move in elevation, Revised May d Stormwater Course - Dynamic Notes: Page 31 of 33

34 11.0 Storage Tanks as Basin or Pipe A storage tank may be modelled as a box culvert or as a basin but do not do both as this will double count the storage. To model the tank with basin areas (12d versions prior to V9c1f) set the pipe diameter to 0.0 For versions V9c1f onwards set conduit type to a Basin link and set the pipe diameter to a value that is meaningful for the long section appearance. It will not affect the calculations. 12d Stormwater Course - Dynamic Notes: Page 32 of 33 Revised May 2010

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