Estudio hidrológico e hidráulico 7 - Puerto Rico · Certificación de Consultor que Completó...

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Estudio hidrológico e hidráulico 7

Transcript of Estudio hidrológico e hidráulico 7 - Puerto Rico · Certificación de Consultor que Completó...

  • Estudio hidrolgico e hidrulico

    7

  • 9 de octubre de 2006

    Federico L. Togni, DirectorPR One, Inc.PO Box 800643Coto Laurel, PR 00780

    RE: HOJA DE TRAMITE:ESTUDIO HIDROLOGICO/HIDRAULICO, CLUB PORTOFINO, NAGUABO, PUERTO RICO

    Estimado ingeniero Togni:

    La siguiente es para someter el estudio hidrolgico e hidrulico final del proyecto de referencia.Se incluyen en este trmite los siguientes documentos:

    1. Dos (2) Originales del Informe H/H Club Portofino, Naguabo, PR. 2. Factura # CHE0604.3. Dos (2) Discos Compactos con Modelos Hidrolgicos e Hidrulicos utilizados en el informe.4. Certificacin de Consultor que Complet Estudio.

    Note que DRNA requiere los planos topogrficos, secciones transversales, y pluvial finaldebidamente sellados y firmados, incluyendo certificacin (carta) del agrimensor en original.Adems, DRNA requiere una carta original del Dueo que autorice al Ing. Jos L. Irizarry Rosaa completar H/H. Finalmente, se debe proveer con copia de la escritura notarizada de lapropiedad. Estos documentos se deben incluir en las carpetas del H/H (ltima seccin delApndice) y junto con el disco compacto, entregarse a Secretara en el DRNA.

    Cordialmente,

    Jos Luis Irizarry Rosa, MCE, PEd.b.a. Caribbean Hydrologic Engineers

    Jos Luis Irizarry Rosa, MECE, PEYadira L. Ayala Ros, PE

    Mansin RealCalle Isabel #205

    Coto Laurel, Puerto Rico 00780 -2600Caribbean Hydrologic Engineers

    Tel. (787) 848-2075 Fax (787) 848-1562Email: [email protected]

  • DETENTION POND DESIGN STUDY: CLUB PORTOFINO PROJECT,

    SECTOR HUCARES, SANTIAGO Y LIMA WARD, MUNICIPALITY OF NAGUABO, PUERTO RICO

    Presented to:

    Federico L. Togni, Director PR One, Inc.

    PO Box 800643 Coto Laurel, Puerto Rico 00780

    October 9, 2006

    Jos Luis Irizarry Rosa, MCE, PE

    Yadira L. Ayala Ros, PE Mansin Real

    205 Calle Isabel Coto Laurel, Puerto Rico 00780-2600

    Tel. (787) 848-2075 Hydrologic Studies Hydraulic Studies Fax. (787) 848-1562

    Water Resources Management Email: [email protected]

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    I. Executive Summary The subject study is part of the design requirements for the proposed Club Portofino in Naguabo, Puerto Rico. The latter consists of the development of a hotel, condo hotel, villas, and sports and service facilities. The project occupies a tract of land of approximately 78.71-acres accessed through a municipal road that conducts to Punta Lima at the Hcares Sector of the Santiago y Lima Ward, Municipality of Naguabo, Puerto Rico. The project is by-passed by two (2) unnamed creeks, one to the West with a basin of about 178.5-acres, and one to the East with about 200.3-acres of watershed area. Both discharge to the Lima Bay which lies to the southeast of the property. To assist in the compliance with the Puerto Rico Planning Board (PRPB) and the Department of Natural and Environmental Resources (DNER) requirements for storm water management, project developer, Eng. Federico Togni, from PR One, Inc., retained our services to evaluate the current and proposed hydrologic conditions of this site, and to determine the corresponding runoff detention system necessary to control excess flows and erosion to be produced by future development. Based on the building distribution, we chose the southeast corner of the property as the ideal location for the detention facilities. The approach will be to develop two (2) independent detention ponds, one for each side of the center ridge that bisects the property. This same divide also applies for the east and west unnamed creeks that travel across the parcel. Therefore each pond will discharge to its corresponding creek just prior their exit from the property. The west pond accounts with a bottom area of 2,558-square meters and a height of 3.75-m. It will be equipped with two (2), 5-ft. X 8-ft. box culvert sections. The east pond includes a 3,226-square meter bottom area with a primary outlet consisting of one (1) box culvert with a 5-ft. X 7-ft. section. Two (2) additional devices, positioned in a multistage structure, are recommended to handle low and intermediate flows. These include an 8-inch diameter pipe positioned at the ponds invert, and two (2), 4-ft. X 5-ft. orifice grates located two (2) feet above the ponds invert. These devices connect to the aforementioned primary outlet structure. Both ponds include side slopes with a 2 Horizontal : 1 Vertical inclination.

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    Table of Contents

    I. Introduction................................................................................................................ 1 II. Study Description.......................................................................................................2 A. Project Location............................................................................................. 2 B. Existing Topography...................................................................................... 2 C. Water Bodies.................................................................................................. 2 D. Problem Description...................................................................................... 2 E. Study Level.................................................................................................... 3 F. Design Conditions.......................................................................................... 3 G. Scope of Work............................................................................................... 4 H. Project Impact................................................................................................ 4 III. Preliminary Evaluation.............................................................................................. 5 A. Visual Inspection of the Site.......................................................................... 5 B. Review of Previous Studies........................................................................... 5 IV. Applied Methodology and Hydrologic Study............................................................6 A. Rainfall Data.................................................................................................. 6 B. Watershed Limits Definition..........................................................................7 C. Bodies of Water Identification....................................................................... 7 D. Topographic Maps......................................................................................... 7 E. Land Use and Vegetation Cover.................................................................... 7 F. Interception and Infiltration........................................................................... 7 G. Unit Hydrograph............................................................................................ 8 H. Summary of Hydrologic Data....................................................................... 9 I. Initial Hydrologic Results.................................................................. 10

    J. Detention Pond Theory................................................................................. 11 K. Detention Pond Parameters............................................................................ 12 L. Final Hydrologic Results............................................................................... 14 V. Conclusions................................................................................................................ 16 VI. Reference................................................................................................................... 17

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    Table of Contents... VII. Appendix....................................................................................................................18

    A. Figures B. Rainfall Distribution, SCS Type II Puerto Rico C. HydroCad Output: Summary of All Rainfall Frequencies and Durations D. HydroCad Output: Detailed Report of Selected Rainfall Frequencies and

    Durations E. Project Drawings: Site Plan, Cross Sections and Details F. Certifications and Submittal Documents

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    List of Tables

    Table 1. Rainfall-Frequency Data for Naguabo, Puerto Rico...................................... 6 Table 2. Existing Conditions Simulation: Physiographic Information Summary....... 10 Table 3. Proposed Conditions Simulation: Physiographic Information Summary...... 10 Table 4. Hydrologic Results Summary: Existing Conditions. 10 Table 5. Hydrologic Results Summary: Proposed Conditions.... 11 Table 6. Summary of Pond and Outlet Parameters: West Portofino Pond.................. 13 Table 7. Summary of Pond and Outlet Parameters: East Portofino Pond.................. 13 Table 8. Hydrologic Results Summary: Proposed Conditions with Ponds............ 14

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    List of Figures: Appendix A Figure 1. Project Schematic Layout Figure 2. Project Location: USGS Naguabo Topo Quadrangle Figure 3. Aerial Color Photo of the Site Figure 4. Project Location: FEMA Map, Naguabo, PR

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    I. Introduction The subject study is part of the design requirements for the proposed Club Portofino in Naguabo, Puerto Rico. The latter consists of the development of a hotel, condo hotel, villas, and sports and service facilities. The project occupies a tract of land of approximately 78.71-acres accessed through a municipal road that conducts to Punta Lima at the Hcares Sector of the Santiago y Lima Ward, Municipality of Naguabo, Puerto Rico. The project is by-passed by two (2) unnamed creeks, one to the West with a basin of about 178.5-acres, and one to the East with about 200.3-acres of watershed area. Both discharge to the Lima Bay which lies to the southeast of the property. Please refer to Figure 1 for the planned site layout of the project. To assist in the compliance with the Puerto Rico Planning Board (PRPB) and the Department of Natural and Environmental Resources (DNER) requirements for storm water management, project developer, Eng. Federico Togni, from PR One, Inc., retained our services to evaluate the current and proposed hydrologic conditions of this site, and to determine the corresponding runoff detention system necessary to control excess flows and erosion to be produced by future development. This report gathers all the related hydrologic and hydraulic observations, documentation, computer models and results for the subject project. The available information submitted by the Owner and used in this document consisted of site plans of the proposed layout.

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    II. Study Description A. Project Location The project is accessed through a municipal road that conducts to Punta Lima at the Hcares Sector of the Santiago y Lima Ward, Municipality of Naguabo, Puerto Rico. It is bounded to the north by the aforementioned municipal road, to the west by various owners, to the east by a PRIDCO property and to the south by the Caribbean Sea. From a hydrologic standpoint, the approximate centroid of the watershed area is located at the North American Datum 1927 coordinates Easting 229,689-m and Northing 39,484-m. A projects site location is included in Figure 2, using the United States Geological Survey (USGS) Topographic Map of the Naguabo Quadrangle (USGS, 1982). B. Existing Topography The existing topographic features of the site can be described as rolling to mountainous as the area is occupied by a pair of ridge formations that downgrade towards the south-southeast. The terrain elevation ranged from 56-m to about one (1) meter near the low lands that connect with the Lima Bay. All elevations are based on the topographic quadrangle of Naguabo, Puerto Rico (USGS, 1982). C. Water Bodies The subject project property accounts with two (2) unnamed creeks. The first lies to the east of the project and includes a hydraulic length of 1,577-meters. The second lies to the west of the property and accounts with a length of 2,088-meters. Both connect to a low land area located towards the south/southeast part of the parcel. The above water bodies eventually discharge to the Caribbean Sea, which lies about 300-meters from the site. D. Problem Description The following items present the problem description of this work.

    1. Rule No. 3 of the PRPB, establishes in Section 14.04 that runoff flows produced by the new development shall not exceed the sites discharge in its existing condition. The project design shall consider this requirement in order to effectively handle the future storm sewer system.

    2. Rule 13 of the PRPB provides requirements for construction on flood zones.

    The project lies outside an AE flood zone identified towards the southeast side of the property (lowlands) according to the Flood Insurance Rate Maps issued by FEMA (April, 2005).

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    3. The Department of Natural and Environmental Resources requested that an assessment be completed with regards to the erosion control measures to be deployed during the construction and operation of the project.

    E. Study Level This investigation is intended to provide the owner and his consultants, with the necessary tools required to review the possible scope, from a water resources viewpoint, of any site improvements, development and/or construction proposed in this area. The study in general accounts with a preliminary character given that adjustments to the current building layout may occur during the design process, therefore, affecting some of the parameters established in this report. Furthermore, the completion of a hydraulics analysis will be necessary once all culvert and /or bridge locations (as applicable), and fill embankments are defined in the design process. In addition, the owner and his consultants shall use this document and its annex deliverables, at their discretion, to pursue the corresponding federal and state agency endorsements and approvals that are usually required for this type of project. F. Design Conditions The hydrologic and hydraulic design of this project will be based on the following criterion and methodology:

    1. Regulatory Documents: the design of the subject work will follow storm sewer management requirements established in the governing rules that apply: Planning Rule No. 3, Reglamento de Lotificacin y Urbanizacin, and Planning Rule No. 13, Reglamento sobre Areas Especiales de Riesgo a Inundacin, all by the Puerto Rico Planning Board (PRPB).

    2. Provided Documents: Eng. Federico Togni submitted a group of documents that

    included preliminary site plans of the project.

    3. Project Overview: the scope of project includes the development of a hotel and residences complex that will occupy a 78.71-acres property.

    4. Proposed Runoff Detention System: this study will consider the design of a

    detention pond system to attenuate the excess flows produced by the new development. In addition, the ponds will serve as the primary erosion control system of the project during construction and operation. This in order to protect the adjacent lowland from man made produced sedimentation.

    5. Proposed Discharge System: the proposed detention ponds will account with

    outlet structures that ultimately will connect to the lower reaches of the unnamed creeks that by-pass the properties and immediately discharge to the Caribbean Sea (Lima Bay), after traveling approximately 300-m through lowlands. To account with a free discharge, the outlet elevation of the discarge pipes must be above the

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    2.2-meters mark. The latter is equivalent to the 100-yr flood elevation of the adjacent AE flood zone.

    G. Scope of Work The main general goals for this investigation can be summarized in the following scope of work:

    1. Determine the hydrological properties of the watershed.

    2. Construct a reasonable mathematical model to perform runoff analysis

    simulations for these watersheds, including existing and proposed conditions.

    3. Construct a reasonable mathematical model to perform storage and outlet structure design and analysis for the required detention pond. This activity includes the selection of the maximum required storage volume, an assessment on ponds location, materials and geometry.

    H. Project Impact The proposed Club Portofino project is currently in the permitting process with local and federal agencies. It is expected to fill a current demand for eco-sensitive, programmed tourist and residential development in the area. Furthermore, the project is also expected to have a positive economic impact in the zone, as several direct and indirect jobs will be required for its construction and operation.

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    III. Preliminary Evaluation A. Visual Inspection of the Site A number of field visits were performed for this Project. These were intended to determine the current land use, topography, water bodies, runoff contributors, and proposed project characteristics involved in this study. These findings can be summarized as follows:

    1. The site currently corresponds to a vacant tract of land. It is mostly covered by brush, pasture and grass.

    2. There are two (2) unnamed creeks that bypass the project. Their channels

    account with dense vegetative cover with few stones and cobbles along their beds. They both discharge to the Lima Bay (Caribbean Sea).

    Please refer to Figure 3 is an aerial color picture of the property. B. Review of Previous Studies No previous, approved hydrologic / hydraulic studies for the particular watershed were identified. As an initial assessment of the hydrologic and hydraulic behavior of the site, the area was checked with respect to the Puerto Rico Planning Board (PRPB) flood zone maps. Upon review with PRPB, the site is not within flood zone AE as identified in FEMAs Flood Insurance Rate Map 72000C1290H. The most adjacent flood area marks a flood elevation of 2.2-m just south/southeast of the property (lowland area). Please refer to Figure 4 for the project location within the FEMA flood map of the area.

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    IV. Applied Methodology and Hydrologic Study Once the problem definition is properly established, the data collection and analysis process was performed. The data collection consisted of the gathering all the applicable hydrologic features of the area by means of field visits, and the revision of available government sources that provided with some of this information. On the other hand, the analysis process involves the mathematical representation of the hydrologic phenomena of the watershed area in order to determine an estimated runoff flow through a known point given a determined rainfall event. From several alternative models, HydroCad was selected as the main simulation engine for this project. It requires the management of sub-models that describe particular processes of the hydrologic cycle. Some of the latter are precipitation (rainfall), interception, infiltration, and unit hydrograph development. A. Rainfall Data The main source for a flood-runoff simulation is the applied rainfall data. The specified rainfall event will ultimately govern the expected runoff flow given constant watershed properties. To obtain a precipitation hyetograph, the accumulated rainfall was estimated at the mass centroid of the watershed area. The National Weather Service Hydrometereological Report Number 42 (or Technical Paper No. 42), was used to determine the accumulated rainfall for the subject storm events. Table 1 describes the accumulated rainfall for all rainfall intensities and durations. Table 1.0 Rainfall-Frequency Data for Naguabo, Puerto Rico (US Weather Bureau, 1961)

    Rainfall Intensity (inches) Frequency (years) 1 2 5 10 25 50 100

    Intensity (hours) 0.5 1.75 2.00 2.60 3.10 3.50 4.00 4.50 1 2.10 2.50 3.30 3.80 4.50 5.00 5.60 2 2.50 3.00 4.10 5.00 5.50 6.50 7.25 3 2.75 3.50 4.50 5.50 6.50 7.25 8.20 6 3.00 4.00 5.60 6.75 8.00 9.20 10.50

    12 3.50 5.00 7.00 8.40 9.50 11.20 13.00 24 4.25 5.75 8.00 10.00 11.50 13.50 15.00

    To perform a temporal distribution of this rainfall, the SCS Type II Puerto Rico rainfall distribution was used. This distribution provides with the typical storm precipitation patterns for the area of Puerto Rico.

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    B. Watershed Limits Definition The watershed considered in this study is defined by the projects property line. The latter will account with natural (ridges) and man-made features (fences and perimeter roads) that will inhibit external flows. The exception will be the two (2) unnamed creeks that cross the property. As envisioned, the projects storm sewer system will connect to a number of detention ponds to be located towards the exiting reaches of these creeks (south/southeast corner of the property). No other storm sewer connection from the project is anticipated at upstream locations of the ponds outlet structures. Therefore, and with the exception of the subject ponds connections, the hydrologic behavior of the creeks watershed areas will not be impacted by the project. Furthermore, a regional analysis of these watershed areas is not necessary since both creeks basically discharge to the Lima Bay immediately after crossing the project. Given the above, the watershed for this study represents the property by itself, which consists of a tract of land of approximately 78.71-acres. C. Bodies of Water Identification As aforementioned throughout this report, there are two (2) unnamed creeks that by pass the subject project. D. Topographic Maps The Naguabo Topographic Quadrangle Map was used to address the terrain and water bodies features for this project. Other sources consisted of maritime zone delimitation plans submitted by Eng. Federico Togni. The subject watershed accounts with sloping patterns that average 13.5 percent in inclination. Maximum elevations were noted at ridge that bisects the property along its center (56-m) while the lower corresponds to the southern and southeastern borders of the parcel (1-m). E. Land Use and Vegetation Cover As described in our Preliminary Evaluation, the site currently corresponds to a vacant tract of land. It is mostly covered by brush, pasture and grass. The proposed conditions land use considered the application of a paved parking and roofs to about 25.7-acres of the total 78.71-acrea of the property. Please refer to Table 2 for a tabulated description of this feature. F. Interception and Infiltration Land surface interception, depression storage and infiltration are referred to in a hydrologic analysis as precipitation losses. These represent the fallen rainfall that does not participate in the

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    runoff process. They are in function of the water storage in trees, brushes, grass, local depressions, cracks, and the infiltration of water to areas beneath the surface, among others. Since the Soil Conservation Service (SCS) interception / infiltration model was used to simulate these hydrologic features within the in-question watershed areas, the Curve Number (CN) of a given sub-basin was determined. To determine the CN, various cover, soil type properties, and the antecedent moisture conditions of the watershed must be effectively determined. The latter were achieved from the revision of the SCS data from Geographical Information Systems, and from our field visits which determine current land use and cover. From the Soil Survey of Naguabo Area Puerto Rico (NRCS, 1979), it arises that the project site accounts with a hydrologic group rating of D (lowest infiltration). Please refer to Table 2 for a quantitative description of these parameters. G. Unit Hydrograph Unit hydrographs are used within the HydroCad sub-basin components to transform the rainfall excess into surface runoff. This hydrograph is synthetically computed from user supplied parameters. HydroCad requires the input of just one subbasin parameter to develop the SCS Dimensionless Unit Hydrograph. This parameter is the Time of Concentration (Tc), which can be subsequently defined as the time required for the outermost fallen raindrop of the sub-basin to hydraulically travel to its exit point. To determine this parameter, the geometric properties of the sub-basin and channels that are related to the flow characteristics of each hydraulic stage must be known. Of several methodologies, the Curve Number Method was selected for the determination of these watersheds Tc. The method is designed for areas of 2,000 acres or less, and is defined by the following variables:

    Tc = T lag / 0.6 ,

    T lag = [ l 0.8 (S+1) 0.7 ] / 1,900 Y 0.5 ,

    S = (1,000 / CN) - 10

    where:

    Tc = Time of Concentration [hours] T lag =Lag time [hours]

    l = Hydraulic length of the watershed [feet] Y = Average land slope [percent]

    S = Potential maximum retention [inches] CN = Weighted Curve Number

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    Note the use of the average land slope, and not the slope of the hydraulic path. Although some care is required to determine this value, the Curve Number method has the advantage of using a small number of fairly objective parameters. This provides more consistent results than some other approaches. The average land slope (or watershed slope) is the slope over an entire land area, rather than the typical slope along the hydraulic path. A theoretical determination of the average land slope requires placing a grid over the area and averaging the slopes for all the squares. The following equation provides a more practical alternative:

    Y = C I / A where:

    Y = Average land slope (rise/run)

    C = Total length of all contour lines I = Contour line interval

    A = Total land area

    For the post-development scenario, the Time of Concentration needs to be determined within the projects own watershed. To consider sheet, shallow and channel (pipe) flows within these zones, the SCS methodology included in the Technical Release No. 55 (TR-55 software) was used. The following equations describe each stage of flow:

    Sheet Flow: Tsf = (0.007 (nL) 0.8) / (P 0.5s 0.4)

    Shallow Concentrated Flow: Tsc = L / (3600 V)

    Channel Flow: Tch = L / (3600 V)

    then, Tc = Tsf + Tsc + Tch where, n = Mannings Roughness Coefficient L = flow length P = 2-year, 24-hour rainfall s = land slope V = average velocity Please refer to Table 2, for a quantitative description of these parameters. H. Summary of Hydrologic Data The following tables summarize the applied hydrological data that was used to simulate the existing and proposed conditions of this project.

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    Table 2.0 Existing Conditions Simulation: Physiographic Information Summary Sub-Basin ID Area

    (acres) Land Use SCS Soil

    Series Weighted

    CN Tc

    (minutes) Club

    Portofino 78.71 Pastures/Grassland/Range

    (Fair Cover) D 80 15.9

    For the proposed conditions, the physiographic information of the Club Portofino basin was adjusted to reflect the change in land use to be provided by the new ground cover. The modifications were based on the proposed residential districts land use, which in turn influenced the Curve Number designation. Similarly, the time of concentration (Tc) was adjusted to reflect the new drainage ways to be produced by the proposed surface and storm sewer system. Please refer to Table 3 for a description of the adjusted physiographic parameters for the proposed conditions. Table 3.0 Proposed Conditions Simulation: Physiographic Information Summary Sub-Basin ID Area

    (acres) Land Use SCS Soil

    Series Weighted

    CN Tc

    (minutes) 25.7 Paved Parking and Roofs Club

    Portofino 53.01 Woods and Grass Combination D 85 6.3

    I. Initial Hydrologic Results As aforementioned, the described hydrologic data and methodology were incorporated in HydroCad interface software. For the subject purposes, two (2) set of results were computed. The first simulates the existing conditions of the subject basin while the second does the same for the pos-development conditions. Table 4.0 Hydrologic Results Summary: Existing Conditions

    Runoff (cfs) Frequency (years) 1 2 5 10 25 50 100

    Intensity (hours) 0.5 110 150 259 360 447 560 677 1 140 204 349 447 591 697 827 2 174 252 440 604 698 889 1035 3 193 304 465 635 808 939 1107 6 192 323 547 713 896 1072 1263

    12 205 366 591 751 877 1071 1275 24 203 318 495 652 769 926 1042

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    Table 5.0 Hydrologic Results Summary: Proposed Conditions

    Runoff (cfs) Frequency (years) 1 2 5 10 25 50 100

    Intensity (hours) 0.5 337 443 721 969 1175 1439 1707 1 421 581 924 1147 1466 1697 1976 2 487 664 1072 1415 1608 1994 2284 3 512 754 1089 1429 1771 2028 2352 6 459 709 1120 1417 1739 2049 2379

    12 392 643 979 1214 1397 1679 1976 24 292 430 635 817 952 1131 1265

    Please note the increase in runoff between existing and proposed conditions, produced by the change in land use for the Club Portofino basin for the subject rainfall event frequencies. J. Detention Pond Theory HydroCAD allows the routing of any hydrograph through a detention pond or reservoir. It requires the set up of the Stage / Storage / Discharge characteristics for a particular pond system. Therefore, for every depth or stage in a pond, there is a corresponding storage and discharge which is based on the properties of the outlet structure and the geometry of the pond. HydroCAD allows specifying up to four (4) unique culvert / orifice structures, four (4) unique weir structures, and exfiltration component and a single tailwater elevation. Each structure can be used as an independent outflow or as part of a multi-stage system. In computing the outflows, HydroCAD treats the operation of these outlet structures as a function of stage or water surface elevation. Partial and full flow conditions are also computed for inlet and outlet control. The equation used for culvert/orifice structures is:

    Q = Co A (2 g hi k) 0.5 (Nb)

    where, Q = discharge in cfs A = culvert area (ft 2 ) hi = distance between the water surface and the centroid of the culvert barrel(1/2 flow depth during partial flow) in feet (Under Inlet Control); Distance between the upstream and downstream water surface (Under Outlet Control) Nb = number of barrels Co = orifice coefficient k = 1 (Under Inlet Control);

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    1.5 + [(29 n2 L) / R1.33] (Under Outlet Control) The basic equation used to calculate weir flow is:

    Q = Cw L H 1.5

    where, Q = discharge in cfs Cw = weir coefficient L = length of the weir crest in ft. H = distance between water surface and the crest in ft. The storage volume is computed by considering a trapezoidal basin where:

    V = L W D + (L + W) Z D 2 + 4/3 Z 2 D 3 where, V = storage at stage D, ft 3 D = stage or depth in ft. L = bottom length in ft. W = bottom width in ft. Z = side slope, (Z:1) (H:V) HydroCAD uses the Storage Indication Method which uses the stage / storage / discharge relationship, and inflow hydrograph and the following relationship: I - O = ds / dt where, I = inflow O = outflow. ds / dt = change in storage K. Detention Pond Parameters Based on the aforementioned building distribution, we chose the southeast corner of the property as the ideal location for the detention facilities. The approach will be to develop two (2) independent detention ponds, one for each side of the center ridge that bisects the property. This same divide also applies for the east and west unnamed creeks that travel across the parcel. Therefore each pond will discharge to its corresponding creek just prior their exit from the property. Using HydroCad features, the following detention pond geometry and outlet structure were simulated for the presented rainfall frequencies and durations. Please refer to Tables 6.0 and 7.0 for a general description of this system features:

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    Table 6.0 Summary of Pond and Outlet Structure Parameters: West Portofino Pond

    Parameter Value

    Storage Method Width, B

    Open Pond 51-m (168-ft)

    Length, L 51-m (168-ft) Height, H

    Side Slopes, Z : 1 3.75-m (12.3-ft)

    2 Material Earth / Grass

    Invert Elevation To be Adjusted to Field Conditions Device 1 (Pond Outlet) Section 5-ft. (H). X 8-ft. (W)

    Device 1 (Pond Outlet) Number of Barrels 2 Device 1 (Pond Outlet) Invert Elevation Equal to Ponds Invert

    Device 1 (Pond Outlet) Maximum Length 15.2-m (50-ft) Device 1 (Pond Outlet) Slope, %. 0.01 Device 1 (Pond Outlet) N-value. 0.013 Device 1 (Pond Outlet) Material

    Minimum Barrel Outlet Invert Elevation Reinforced Concrete

    As per Shown Outlet Slope Table 7.0 Summary of Pond and Outlet Structure Parameters: East Portofino Pond

    Parameter Value

    Storage Method Bottom Width, B

    Open Pond 57-m (187-ft)

    Bottom Length, L 57-m (187-ft) Height, H

    Side Slopes, Z : 1 5.25-m (17.3-ft)

    2 Material Earth / Grass

    Device 1 (Pond Outlet) Section 5-ft. (H). X 7-ft. (W) Device 1 (Pond Outlet) Number of Barrels 1

    Device 1 (Pond Outlet) Invert Elevation Equal to Ponds Invert Device 1 (Pond Outlet) Maximum Length 15.2-m (50-ft)

    Device 1 (Pond Outlet) Slope, %. 0.01 Device 1 (Pond Outlet) N-value. 0.013 Device 1 (Pond Outlet) Material

    Minimum Barrel Outlet Invert Elevation Reinforced Concrete

    As per Shown Outlet Slope Device 2 (Low Flow) Diameter 0.20-m (8-in.)

    Device 2 (Low Flow) Number of Barrels 1 Device 2 (Low Flow) Invert Elevation 2.4-m (8-ft)

    Device 2 (Low Flow) Length 1-ft Device 2 (Low Flow) Material Reinforced Concrete

    Device 3 (Grate) Section 4-ft. (H). X 5-ft. (W) Device 3 (Grate) Number of Barrels 2

    Device 3 (Grate) Invert Elevation 0.6 (10-ft) Above Ponds Invert Device 3 (Grate) Length 1-ft

    Device 3 (Grate) Material Reinforced Concrete

  • Detention Pond Study, Club Portofino Project, Santiago y Lima Ward, Naguabo, Puerto Rico

    Caribbean Hydrologic Engineers 14

    Please note that the bottom, width and height dimensions of the pond may be adjusted to accommodate other geometries, as long as the computed storage volume is not altered. In any case, a final revision of this study shall be completed once final grading and site data is available. In addition, the ponds shall be equipped with the corresponding pilot channels that enable flows to travel from storm sewer pipe outlets to the ponds outlet structure. All outlet structure devices shall account with debris racks and grates in order to avoid waste transport downstream of the pond. Furthermore, the pond shall account with vehicle access ramps appropriate for maintenance tasks. All top of pond perimeter shall include the corresponding access control fences and gates (minimum height of 4-ft.). Please refer to the Appendix of this report for the corresponding drawings and outlet structures detail schematics. L. Final Hydrologic Results Table 7 presents the hydrologic results for the existing and proposed with detention pond conditions of the subject project. Table 8.0 Hydrologic Results Summary: Proposed Conditions with Ponds

    Runoff (cfs) Frequency (years) 1 2 5 10 25 50 100 Intensity (hours)

    0.5 88 121 211 293 364 465 577 1 114 169 286 367 498 602 733 2 144 206 358 509 601 795 937 3 159 248 380 539 713 848 1002 6 158 259 454 621 812 993 1148

    12 166 291 514 684 820 1025 1194 24 160 261 447 616 741 902 1019

    Please note that the comparison between the pre-development, post-development and post-development with reservoir scenarios runoff indicates that all post development flows with reservoir are less or equal to the pre-development flows. Therefore, the above detention system complies with Puerto Rico Planning Board criterion for new developments. For a full description of all input data and results output and graphs, please refer to the Appendix of this document.

  • Detention Pond Study, Club Portofino Project, Santiago y Lima Ward, Naguabo, Puerto Rico

    Caribbean Hydrologic Engineers 16

    VI. References

    1. USGS, Topographic Map of the Naguabo Quadrangle, United States Geological Survey, Washington, D.C., 1982.

    2. Puerto Rico Planning Board, Rule Number 3, Reglamento de Lotificacin y

    Urbanizacin. 2001

    3. Federal Emergency Management Administration (FEMA). Flood Insurance Rate Map (FIRM), Naguabo, Puerto Rico.

    4. National Resources Conservation Service (NRCS), Technical Release 55 Urban

    Hydrology for Small Watershed. 1986.

    5. US Army Corps of Engineers, Hydrologic Engineering Center, HEC-HMS Hydrologic Modeling Software, Users Manual. 1997.

    6. Intellisolve, HydroCad 8.0, Owners Manual. 2006.

    7. U.S. Weather Bureau, Generalized Estimates of Probable Maximum Precipitation and

    Rainfall Frequency Data for Puerto Rico and Virgin Islands (Technical Paper No. 42), U.S. Department of Commerce, Washington, D.C., 1961.

    8. National Resources Conservation Service (NRCS), Soil Survey of Humacao Area of

    Eastern Puerto Rico. 1979.

    9. Singh, V. Elementary Hydrology, Prentice Hall, Englewood Cliffs, New Jersey. 1992.

    10. Gribbin, J. Introduction to Hydraulics and Hydrology, Delmar, Albany, NY. 1997.

    11. Haestad, Durrans. Stormwater Conveyance Modeling and Design, Haestad Press, Waterbury, CT. 2003

    12. US Army Corps of Engineers, Hydrologic Engineering Center, HEC-RAS River Analysis

    System, Users Manual. 1997.

  • Detention Pond Study, Club Portofino Project, Santiago y Lima Ward, Naguabo, Puerto Rico

    Caribbean Hydrologic Engineers 17

    VII. Appendix

  • Detention Pond Study, Club Portofino Project, Santiago y Lima Ward, Naguabo, Puerto Rico

    Caribbean Hydrologic Engineers 1

    A. Figures

  • !"

  • Detention Pond Study, Club Portofino Project, Santiago y Lima Ward, Naguabo, Puerto Rico

    Caribbean Hydrologic Engineers 2

    B. Rainfall Distribution: SCS Type II Puerto Rico

  • // HydroCAD Rainfall table// Copyright (c) 2004 HydroCAD Software Solutions LLC// DO NOT MIDIFY THIS FILE! For details see Rainfall.txt

    name=Type II 24-hr Tabulartimeunits=hoursduration=24comment=Type II 24-hour tabular mass curve to match TR-20smoothing=false

    depth=.000 .002 .005 .008 .011 .014 .017 .02 .023 .026depth=.029 .032 .035 .038 .041 .044 .048 .052 .056 .060depth=.064 .068 .072 .076 .080 .085 .090 .095 .100 .105depth=.110 .115 .120 .126 .133 .140 .147 .155 .163 .172depth=.181 .191 .203 .218 .236 .257 .283 .387 .663 .707depth=.735 .758 .776 .791 .804 .815 .825 .834 .842 .849depth=.856 .863 .869 .875 .881 .887 .893 .898 .903 .908depth=.913 .918 .922 .926 .930 .934 .938 .942 .946 .950depth=.953 .956 .959 .962 .965 .968 .971 .974 .977 .980depth=.983 .986 .989 .992 .995 .998 1.000

  • Detention Pond Study, Club Portofino Project, Santiago y Lima Ward, Naguabo, Puerto Rico

    Caribbean Hydrologic Engineers 3

    C. HydroCad Output: Summary of All Rainfall Frequencies and Durations

  • 1S

    Clu

    b P

    orto

    fino

    Pro

    ject

    Pre

    Dev

    4S

    Wes

    t Clu

    b P

    orto

    fino

    Pro

    ject

    Pos

    t Dev

    6S

    Eas

    t Clu

    b P

    orto

    fino

    Pro

    ject

    Pos

    t Dev

    7S

    Tota

    l Clu

    b P

    orto

    fino

    Pro

    ject

    Pos

    t Dev

    5P

    Wes

    t Por

    tofin

    o P

    ond

    8P

    Eas

    t Por

    tofin

    o P

    ond

    9L

    Com

    bine

    d P

    ost D

    ev O

    utle

    t

    Dra

    inag

    e D

    iagr

    am fo

    r Nag

    uabo

    Pla

    ya P

    roje

    ctP

    repa

    red

    by C

    arib

    bean

    Hyd

    rolo

    gic

    Eng

    inee

    rs

    1

    0/18

    /200

    6H

    ydro

    CA

    D

    8.0

    0 s

    /n 0

    0330

    9

    200

    6 H

    ydro

    CA

    D S

    oftw

    are

    Sol

    utio

    ns L

    LC

    Sub

    cat

    Rea

    chP

    ond

    Link

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -1yr

    Rai

    nfal

    l=2.

    10"

    Nag

    uabo

    Pla

    ya P

    roje

    ctP

    age

    2P

    repa

    red

    by C

    arib

    bean

    Hyd

    rolo

    gic

    Eng

    inee

    rs10

    /18/

    2006

    Hyd

    roC

    AD

    8

    .00

    s/n

    003

    309

    2

    006

    Hyd

    roC

    AD

    Sof

    twar

    e S

    olut

    ions

    LLC

    Subc

    atch

    men

    t 1S:

    Clu

    b Po

    rtof

    ino

    Proj

    ect P

    re D

    ev

    Run

    off

    =13

    9.84

    cfs

    @

    0.72

    hrs

    , V

    olum

    e=4.

    095

    af,

    Dep

    th=

    0.62

    "

    Run

    off b

    y S

    CS

    TR

    -20

    met

    hod,

    UH

    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -1yr

    Rai

    nfal

    l=2.

    10"

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n78

    .710

    80P

    astu

    re/g

    rass

    land

    /rang

    e, G

    ood,

    HS

    G D

    78.7

    10P

    ervi

    ous

    Are

    a

    TcLe

    ngth

    Slo

    peV

    eloc

    ityC

    apac

    ityD

    escr

    iptio

    n(m

    in)

    (feet

    )(ft

    /ft)

    (ft/s

    ec)

    (cfs

    )15

    .92,

    145

    0.13

    502.

    24La

    g/C

    N M

    etho

    d,

    Con

    tour

    Len

    gth=

    14,

    026'

    Int

    erva

    l= 3

    3'

    Subc

    atch

    men

    t 4S:

    Wes

    t Clu

    b Po

    rtof

    ino

    Proj

    ect P

    ost D

    ev

    Run

    off

    =27

    4.39

    cfs

    @

    0.58

    hrs

    , V

    olum

    e=3.

    716

    af,

    Dep

    th=

    0.87

    "

    Run

    off b

    y S

    CS

    TR

    -20

    met

    hod,

    UH

    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -1yr

    Rai

    nfal

    l=2.

    10"

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n16

    .780

    98P

    aved

    par

    king

    & ro

    ofs

    34.5

    2079

    Woo

    ds/g

    rass

    com

    b., G

    ood,

    HS

    G D

    51.3

    0085

    Wei

    ghte

    d A

    vera

    ge34

    .520

    Per

    viou

    s A

    rea

    16.7

    80Im

    perv

    ious

    Are

    a

    TcLe

    ngth

    Slo

    peV

    eloc

    ityC

    apac

    ityD

    escr

    iptio

    n(m

    in)

    (feet

    )(ft

    /ft)

    (ft/s

    ec)

    (cfs

    )4.

    690

    0.13

    500.

    33Sh

    eet F

    low

    , New

    Lan

    dsca

    peG

    rass

    : Den

    se

    n= 0

    .240

    P

    2= 5

    .75"

    0.1

    500.

    1350

    7.46

    Shal

    low

    Con

    cent

    rate

    d Fl

    ow,

    Pav

    ed

    Kv=

    20.

    3 fp

    s1.

    62,

    089

    0.13

    5021

    .84

    38.6

    0C

    ircul

    ar C

    hann

    el (p

    ipe)

    , Fro

    m C

    urb

    to O

    utle

    tD

    iam

    = 18

    .0"

    Are

    a= 1

    .8 s

    f P

    erim

    = 4.

    7' r

    = 0.

    38'

    n= 0

    .013

    Con

    cret

    e pi

    pe, b

    ends

    & c

    onne

    ctio

    ns6.

    32,

    229

    Tota

    l

    Subc

    atch

    men

    t 6S:

    Eas

    t Clu

    b Po

    rtof

    ino

    Proj

    ect P

    ost D

    ev

    Run

    off

    =14

    6.56

    cfs

    @

    0.58

    hrs

    , V

    olum

    e=1.

    985

    af,

    Dep

    th=

    0.87

    "

    Run

    off b

    y S

    CS

    TR

    -20

    met

    hod,

    UH

    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -1yr

    Rai

    nfal

    l=2.

    10"

  • Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -1yr

    Rai

    nfal

    l=2.

    10"

    Nag

    uabo

    Pla

    ya P

    roje

    ctP

    age

    3P

    repa

    red

    by C

    arib

    bean

    Hyd

    rolo

    gic

    Eng

    inee

    rs10

    /18/

    2006

    Hyd

    roC

    AD

    8

    .00

    s/n

    003

    309

    2

    006

    Hyd

    roC

    AD

    Sof

    twar

    e S

    olut

    ions

    LLC

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n8.

    960

    98P

    aved

    par

    king

    & ro

    ofs

    18.4

    4079

    Woo

    ds/g

    rass

    com

    b., G

    ood,

    HS

    G D

    27.4

    0085

    Wei

    ghte

    d A

    vera

    ge18

    .440

    Per

    viou

    s A

    rea

    8.96

    0Im

    perv

    ious

    Are

    a

    TcLe

    ngth

    Slo

    peV

    eloc

    ityC

    apac

    ityD

    escr

    iptio

    n(m

    in)

    (feet

    )(ft

    /ft)

    (ft/s

    ec)

    (cfs

    )4.

    690

    0.13

    500.

    33Sh

    eet F

    low

    , New

    Lan

    dsca

    peG

    rass

    : Den

    se

    n= 0

    .240

    P

    2= 5

    .75"

    0.1

    500.

    1350

    7.46

    Shal

    low

    Con

    cent

    rate

    d Fl

    ow,

    Pav

    ed

    Kv=

    20.

    3 fp

    s1.

    62,

    089

    0.13

    5021

    .84

    38.6

    0C

    ircul

    ar C

    hann

    el (p

    ipe)

    , Fro

    m C

    urb

    to O

    utle

    tD

    iam

    = 18

    .0"

    Are

    a= 1

    .8 s

    f P

    erim

    = 4.

    7' r

    = 0.

    38'

    n= 0

    .013

    Con

    cret

    e pi

    pe, b

    ends

    & c

    onne

    ctio

    ns6.

    32,

    229

    Tota

    l

    Subc

    atch

    men

    t 7S:

    Tot

    al C

    lub

    Port

    ofin

    o Pr

    ojec

    t Pos

    t Dev

    Run

    off

    =42

    1.00

    cfs

    @

    0.58

    hrs

    , V

    olum

    e=5.

    701

    af,

    Dep

    th=

    0.87

    "

    Run

    off b

    y S

    CS

    TR

    -20

    met

    hod,

    UH

    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -1yr

    Rai

    nfal

    l=2.

    10"

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n25

    .700

    98P

    aved

    par

    king

    & ro

    ofs

    53.0

    1079

    Woo

    ds/g

    rass

    com

    b., G

    ood,

    HS

    G D

    78.7

    1085

    Wei

    ghte

    d A

    vera

    ge53

    .010

    Per

    viou

    s A

    rea

    25.7

    00Im

    perv

    ious

    Are

    a

    TcLe

    ngth

    Slo

    peV

    eloc

    ityC

    apac

    ityD

    escr

    iptio

    n(m

    in)

    (feet

    )(ft

    /ft)

    (ft/s

    ec)

    (cfs

    )4.

    690

    0.13

    500.

    33Sh

    eet F

    low

    , New

    Lan

    dsca

    peG

    rass

    : Den

    se

    n= 0

    .240

    P

    2= 5

    .75"

    0.1

    500.

    1350

    7.46

    Shal

    low

    Con

    cent

    rate

    d Fl

    ow,

    Pav

    ed

    Kv=

    20.

    3 fp

    s1.

    62,

    089

    0.13

    5021

    .84

    38.6

    0C

    ircul

    ar C

    hann

    el (p

    ipe)

    , Fro

    m C

    urb

    to O

    utle

    tD

    iam

    = 18

    .0"

    Are

    a= 1

    .8 s

    f P

    erim

    = 4.

    7' r

    = 0.

    38'

    n= 0

    .013

    Con

    cret

    e pi

    pe, b

    ends

    & c

    onne

    ctio

    ns6.

    32,

    229

    Tota

    l

    Pond

    5P:

    Wes

    t Por

    tofin

    o Po

    nd

    Inflo

    w A

    rea

    =51

    .300

    ac,

    Inf

    low

    Dep

    th =

    0.

    87"

    for

    Nag

    1H

    R-1

    yr e

    vent

    Inflo

    w=

    274.

    39 c

    fs @

    0.

    58 h

    rs,

    Vol

    ume=

    3.71

    6 af

    Out

    flow

    =11

    3.25

    cfs

    @

    0.66

    hrs

    , V

    olum

    e=3.

    716

    af,

    Atte

    n= 5

    9%,

    Lag=

    5.0

    min

    Prim

    ary

    =11

    3.25

    cfs

    @

    0.66

    hrs

    , V

    olum

    e=3.

    716

    af

    Rou

    ting

    by S

    tor-

    Ind

    met

    hod,

    Tim

    e S

    pan=

    0.0

    0-24

    .00

    hrs,

    dt=

    0.0

    1 hr

    s

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -1yr

    Rai

    nfal

    l=2.

    10"

    Nag

    uabo

    Pla

    ya P

    roje

    ctP

    age

    4P

    repa

    red

    by C

    arib

    bean

    Hyd

    rolo

    gic

    Eng

    inee

    rs10

    /18/

    2006

    Hyd

    roC

    AD

    8

    .00

    s/n

    003

    309

    2

    006

    Hyd

    roC

    AD

    Sof

    twar

    e S

    olut

    ions

    LLC

    Pea

    k E

    lev=

    9.6

    9' @

    0.6

    6 hr

    s S

    urf.A

    rea=

    0.9

    69 a

    c S

    tora

    ge=

    1.58

    6 af

    Plu

    g-Fl

    ow d

    eten

    tion

    time=

    14.

    1 m

    in c

    alcu

    late

    d fo

    r 3.7

    14 a

    f (10

    0% o

    f inf

    low

    )C

    ente

    r-of

    -Mas

    s de

    t. tim

    e= 1

    4.2

    min

    ( 54

    .9 -

    40.7

    )

    Vol

    ume

    Inve

    rtA

    vail.

    Sto

    rage

    Sto

    rage

    Des

    crip

    tion

    #18.

    00'

    9.12

    4 af

    150.

    00'W

    x 2

    62.4

    0'L

    x 8.

    50'H

    46m

    X80m

    X2.5

    9m Z

    =2.0

    Dev

    ice

    Rou

    ting

    Inve

    rtO

    utle

    t Dev

    ices

    #1P

    rimar

    y8.

    00'

    8.00

    ' W x

    5.0

    0' H

    x 5

    0.0'

    long

    Cul

    vert

    X 2

    .00

    R

    CP

    , squ

    are

    edge

    hea

    dwal

    l, K

    e= 0

    .500

    O

    utle

    t Inv

    ert=

    7.5

    0'

    S=

    0.01

    00 '/

    ' C

    c= 0

    .900

    n=

    0.0

    13 C

    oncr

    ete

    pipe

    , ben

    ds &

    con

    nect

    ions

    Prim

    ary

    Out

    Flow

    Max

    =113

    .10

    cfs

    @ 0

    .66

    hrs

    HW

    =9.6

    9'

    (Fre

    e D

    isch

    arge

    )1=

    Cul

    vert

    (Inl

    et C

    ontro

    ls 1

    13.1

    0 cf

    s @

    4.1

    8 fp

    s)

    Pond

    8P:

    Eas

    t Por

    tofin

    o Po

    nd

    Inflo

    w A

    rea

    =27

    .400

    ac,

    Inf

    low

    Dep

    th =

    0.

    87"

    for

    Nag

    1H

    R-1

    yr e

    vent

    Inflo

    w=

    146.

    56 c

    fs @

    0.

    58 h

    rs,

    Vol

    ume=

    1.98

    5 af

    Out

    flow

    =1.

    56 c

    fs @

    1.

    15 h

    rs,

    Vol

    ume=

    1.55

    3 af

    , A

    tten=

    99%

    , La

    g= 3

    3.9

    min

    Prim

    ary

    =1.

    56 c

    fs @

    1.

    15 h

    rs,

    Vol

    ume=

    1.55

    3 af

    Rou

    ting

    by S

    tor-

    Ind

    met

    hod,

    Tim

    e S

    pan=

    0.0

    0-24

    .00

    hrs,

    dt=

    0.0

    1 hr

    sP

    eak

    Ele

    v= 9

    .19'

    @ 1

    .15

    hrs

    Sur

    f.Are

    a= 1

    .639

    ac

    Sto

    rage

    = 1.

    916

    af

    Plu

    g-Fl

    ow d

    eten

    tion

    time=

    494

    .3 m

    in c

    alcu

    late

    d fo

    r 1.5

    53 a

    f (78

    % o

    f inf

    low

    )C

    ente

    r-of

    -Mas

    s de

    t. tim

    e= 4

    90.4

    min

    ( 53

    1.1

    - 40.

    7 )

    Vol

    ume

    Inve

    rtA

    vail.

    Sto

    rage

    Sto

    rage

    Des

    crip

    tion

    #18.

    00'

    15.2

    52 a

    f26

    2.40

    'W x

    262

    .40'

    L x

    8.50

    'H 8

    0mX8

    0mX2

    .59m

    Z=2

    .0

    Dev

    ice

    Rou

    ting

    Inve

    rtO

    utle

    t Dev

    ices

    #1P

    rimar

    y8.

    00'

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    ' W x

    5.0

    0' H

    x 5

    0.0'

    long

    Cul

    vert

    R

    CP

    , squ

    are

    edge

    hea

    dwal

    l, K

    e= 0

    .500

    O

    utle

    t Inv

    ert=

    7.5

    0'

    S=

    0.01

    00 '/

    ' C

    c= 0

    .900

    n=

    0.0

    13 C

    oncr

    ete

    pipe

    , ben

    ds &

    con

    nect

    ions

    #2

    Dev

    ice

    18.

    00'

    8.0"

    Ver

    t. O

    rific

    e/G

    rate

    C=

    0.60

    0

    #3D

    evic

    e 1

    10.0

    0'5.

    00' W

    x 4

    .00'

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    ert.

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    ice/

    Gra

    te X

    2.0

    0 C

    = 0.

    600

    Prim

    ary

    Out

    Flow

    Max

    =1.5

    6 cf

    s @

    1.1

    5 hr

    s H

    W=9

    .19'

    (F

    ree

    Dis

    char

    ge)

    1=C

    ulve

    rt (P

    asse

    s 1.

    56 c

    fs o

    f 29.

    19 c

    fs p

    oten

    tial f

    low

    )2=

    Orif

    ice/

    Gra

    te (

    Orif

    ice

    Con

    trols

    1.5

    6 cf

    s @

    4.4

    6 fp

    s)3=

    Orif

    ice/

    Gra

    te (

    Con

    trols

    0.0

    0 cf

    s)

  • Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -1yr

    Rai

    nfal

    l=2.

    10"

    Nag

    uabo

    Pla

    ya P

    roje

    ctP

    age

    5P

    repa

    red

    by C

    arib

    bean

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    gic

    Eng

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    rs10

    /18/

    2006

    Hyd

    roC

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    8

    .00

    s/n

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    309

    2

    006

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    Sof

    twar

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    ions

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    Com

    bine

    d Po

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    ev O

    utle

    t

    Inflo

    w A

    rea

    =78

    .700

    ac,

    Inf

    low

    Dep

    th >

    0.

    80"

    for

    Nag

    1H

    R-1

    yr e

    vent

    Inflo

    w=

    114.

    36 c

    fs @

    0.

    66 h

    rs,

    Vol

    ume=

    5.26

    9 af

    Prim

    ary

    =11

    4.36

    cfs

    @

    0.66

    hrs

    , V

    olum

    e=5.

    269

    af,

    Atte

    n= 0

    %,

    Lag=

    0.0

    min

    Prim

    ary

    outfl

    ow =

    Inflo

    w, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -25y

    r R

    ainf

    all=

    4.50

    "N

    agua

    bo P

    laya

    Pro

    jec

    Pag

    e 6

    Pre

    pare

    d by

    Car

    ibbe

    an H

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    c E

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    10/1

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    06H

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    8.0

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    6 H

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    off

    =59

    0.65

    cfs

    @

    0.71

    hrs

    , V

    olum

    e=16

    .146

    af,

    Dep

    th=

    2.46

    "

    Run

    off b

    y S

    CS

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    met

    hod,

    UH

    =SC

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    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -25y

    r R

    ainf

    all=

    4.50

    "

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n78

    .710

    80P

    astu

    re/g

    rass

    land

    /rang

    e, G

    ood,

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    G D

    78.7

    10P

    ervi

    ous

    Are

    a

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    ityD

    escr

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    n(m

    in)

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    )(ft

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    ec)

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    .92,

    145

    0.13

    502.

    24La

    g/C

    N M

    etho

    d,

    Con

    tour

    Len

    gth=

    14,

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    Proj

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    =95

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    0.58

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    olum

    e=12

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    af,

    Dep

    th=

    2.91

    "

    Run

    off b

    y S

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    TR

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    met

    hod,

    UH

    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -25y

    r R

    ainf

    all=

    4.50

    "

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n16

    .780

    98P

    aved

    par

    king

    & ro

    ofs

    34.5

    2079

    Woo

    ds/g

    rass

    com

    b., G

    ood,

    HS

    G D

    51.3

    0085

    Wei

    ghte

    d A

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    .520

    Per

    viou

    s A

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    16.7

    80Im

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    Are

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    n(m

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    , New

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    se

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    7.46

    Shal

    low

    Con

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    ow,

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    ed

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    62,

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    0.13

    5021

    .84

    38.6

    0C

    ircul

    ar C

    hann

    el (p

    ipe)

    , Fro

    m C

    urb

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    utle

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    iam

    = 18

    .0"

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    a= 1

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    onne

    ctio

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    32,

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    ino

    Proj

    ect P

    ost D

    ev

    Run

    off

    =51

    0.39

    cfs

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    hrs

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    olum

    e=6.

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    af,

    Dep

    th=

    2.91

    "

    Run

    off b

    y S

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    met

    hod,

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    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -25y

    r R

    ainf

    all=

    4.50

    "

  • Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -25y

    r R

    ainf

    all=

    4.50

    "N

    agua

    bo P

    laya

    Pro

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    Pag

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    Pre

    pare

    d by

    Car

    ibbe

    an H

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    c E

    ngin

    eers

    10/1

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    06H

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    8.0

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    200

    6 H

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    are

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    ns L

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    iptio

    n8.

    960

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    par

    king

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    ofs

    18.4

    4079

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    b., G

    ood,

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    G D

    27.4

    0085

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    ghte

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    .440

    Per

    viou

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    Are

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    n(m

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    690

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    se

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    P

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    7.46

    Shal

    low

    Con

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    ed

    Kv=

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    62,

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    0.13

    5021

    .84

    38.6

    0C

    ircul

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    el (p

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    Tota

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    Run

    off

    =1,

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    16 c

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    0.

    58 h

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    ume=

    19.0

    81 a

    f, D

    epth

    =2.

    91"

    Run

    off b

    y S

    CS

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    -20

    met

    hod,

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    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -25y

    r R

    ainf

    all=

    4.50

    "

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n25

    .700

    98P

    aved

    par

    king

    & ro

    ofs

    53.0

    1079

    Woo

    ds/g

    rass

    com

    b., G

    ood,

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    G D

    78.7

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    Wei

    ghte

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    (feet

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    33Sh

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    7.46

    Shal

    low

    Con

    cent

    rate

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    ed

    Kv=

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    3 fp

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    62,

    089

    0.13

    5021

    .84

    38.6

    0C

    ircul

    ar C

    hann

    el (p

    ipe)

    , Fro

    m C

    urb

    to O

    utle

    tD

    iam

    = 18

    .0"

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    .8 s

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    n= 0

    .013

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    ends

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    ctio

    ns6.

    32,

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    l

    Pond

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    t Por

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    nd

    Inflo

    w A

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    =51

    .300

    ac,

    Inf

    low

    Dep

    th =

    2.

    91"

    for

    Nag

    1H

    R-2

    5yr e

    vent

    Inflo

    w=

    955.

    58 c

    fs @

    0.

    58 h

    rs,

    Vol

    ume=

    12.4

    37 a

    fO

    utflo

    w=

    483.

    80 c

    fs @

    0.

    64 h

    rs,

    Vol

    ume=

    12.4

    37 a

    f, A

    tten=

    49%

    , La

    g= 3

    .7 m

    inP

    rimar

    y=

    483.

    80 c

    fs @

    0.

    64 h

    rs,

    Vol

    ume=

    12.4

    37 a

    f

    Rou

    ting

    by S

    tor-

    Ind

    met

    hod,

    Tim

    e S

    pan=

    0.0

    0-24

    .00

    hrs,

    dt=

    0.0

    1 hr

    s

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -25y

    r R

    ainf

    all=

    4.50

    "N

    agua

    bo P

    laya

    Pro

    jec

    Pag

    e 8

    Pre

    pare

    d by

    Car

    ibbe

    an H

    ydro

    logi

    c E

    ngin

    eers

    10/1

    8/20

    06H

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    8.0

    0 s

    /n 0

    0330

    9

    200

    6 H

    ydro

    CA

    D S

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    are

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    utio

    ns L

    LC

    Pea

    k E

    lev=

    12.

    86' @

    0.6

    4 hr

    s S

    urf.A

    rea=

    1.0

    96 a

    c S

    tora

    ge=

    4.85

    2 af

    Plu

    g-Fl

    ow d

    eten

    tion

    time=

    9.7

    min

    cal

    cula

    ted

    for 1

    2.43

    7 af

    (100

    % o

    f inf

    low

    )C

    ente

    r-of

    -Mas

    s de

    t. tim

    e= 9

    .5 m

    in (

    48.8

    - 39

    .3 )

    Vol

    ume

    Inve

    rtA

    vail.

    Sto

    rage

    Sto

    rage

    Des

    crip

    tion

    #18.

    00'

    9.12

    4 af

    150.

    00'W

    x 2

    62.4

    0'L

    x 8.

    50'H

    46m

    X80m

    X2.5

    9m Z

    =2.0

    Dev

    ice

    Rou

    ting

    Inve

    rtO

    utle

    t Dev

    ices

    #1P

    rimar

    y8.

    00'

    8.00

    ' W x

    5.0

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    x 5

    0.0'

    long

    Cul

    vert

    X 2

    .00

    R

    CP

    , squ

    are

    edge

    hea

    dwal

    l, K

    e= 0

    .500

    O

    utle

    t Inv

    ert=

    7.5

    0'

    S=

    0.01

    00 '/

    ' C

    c= 0

    .900

    n=

    0.0

    13 C

    oncr

    ete

    pipe

    , ben

    ds &

    con

    nect

    ions

    Prim

    ary

    Out

    Flow

    Max

    =483

    .48

    cfs

    @ 0

    .64

    hrs

    HW

    =12.

    86'

    (Fre

    e D

    isch

    arge

    )1=

    Cul

    vert

    (Bar

    rel C

    ontro

    ls 4

    83.4

    8 cf

    s @

    8.2

    9 fp

    s)

    Pond

    8P:

    Eas

    t Por

    tofin

    o Po

    nd

    Inflo

    w A

    rea

    =27

    .400

    ac,

    Inf

    low

    Dep

    th =

    2.

    91"

    for

    Nag

    1H

    R-2

    5yr e

    vent

    Inflo

    w=

    510.

    39 c

    fs @

    0.

    58 h

    rs,

    Vol

    ume=

    6.64

    3 af

    Out

    flow

    =43

    .90

    cfs

    @

    0.88

    hrs

    , V

    olum

    e=5.

    822

    af,

    Atte

    n= 9

    1%,

    Lag=

    18.

    1 m

    inP

    rimar

    y=

    43.9

    0 cf

    s @

    0.

    88 h

    rs,

    Vol

    ume=

    5.82

    2 af

    Rou

    ting

    by S

    tor-

    Ind

    met

    hod,

    Tim

    e S

    pan=

    0.0

    0-24

    .00

    hrs,

    dt=

    0.0

    1 hr

    sP

    eak

    Ele

    v= 1

    1.18

    ' @ 0

    .88

    hrs

    Sur

    f.Are

    a= 1

    .738

    ac

    Sto

    rage

    = 5.

    271

    af

    Plu

    g-Fl

    ow d

    eten

    tion

    time=

    315

    .0 m

    in c

    alcu

    late

    d fo

    r 5.8

    22 a

    f (88

    % o

    f inf

    low

    )C

    ente

    r-of

    -Mas

    s de

    t. tim

    e= 3

    12.5

    min

    ( 35

    1.8

    - 39.

    3 )

    Vol

    ume

    Inve

    rtA

    vail.

    Sto

    rage

    Sto

    rage

    Des

    crip

    tion

    #18.

    00'

    15.2

    52 a

    f26

    2.40

    'W x

    262

    .40'

    L x

    8.50

    'H 8

    0mX8

    0mX2

    .59m

    Z=2

    .0

    Dev

    ice

    Rou

    ting

    Inve

    rtO

    utle

    t Dev

    ices

    #1P

    rimar

    y8.

    00'

    7.00

    ' W x

    5.0

    0' H

    x 5

    0.0'

    long

    Cul

    vert

    R

    CP

    , squ

    are

    edge

    hea

    dwal

    l, K

    e= 0

    .500

    O

    utle

    t Inv

    ert=

    7.5

    0'

    S=

    0.01

    00 '/

    ' C

    c= 0

    .900

    n=

    0.0

    13 C

    oncr

    ete

    pipe

    , ben

    ds &

    con

    nect

    ions

    #2

    Dev

    ice

    18.

    00'

    8.0"

    Ver

    t. O

    rific

    e/G

    rate

    C=

    0.60

    0

    #3D

    evic

    e 1

    10.0

    0'5.

    00' W

    x 4

    .00'

    H V

    ert.

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    ice/

    Gra

    te X

    2.0

    0 C

    = 0.

    600

    Prim

    ary

    Out

    Flow

    Max

    =43.

    88 c

    fs @

    0.8

    8 hr

    s H

    W=1

    1.18

    ' (F

    ree

    Dis

    char

    ge)

    1=C

    ulve

    rt (P

    asse

    s 43

    .88

    cfs

    of 1

    18.4

    1 cf

    s po

    tent

    ial f

    low

    )2=

    Orif

    ice/

    Gra

    te (

    Orif

    ice

    Con

    trols

    2.8

    3 cf

    s @

    8.1

    2 fp

    s)3=

    Orif

    ice/

    Gra

    te (

    Orif

    ice

    Con

    trols

    41.

    04 c

    fs @

    3.4

    8 fp

    s)

  • Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -25y

    r R

    ainf

    all=

    4.50

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    agua

    bo P

    laya

    Pro

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    Pag

    e 9

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    pare

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    bine

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    =78

    .700

    ac,

    Inf

    low

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    th >

    2.

    78"

    for

    Nag

    1H

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    5yr e

    vent

    Inflo

    w=

    498.

    33 c

    fs @

    0.

    64 h

    rs,

    Vol

    ume=

    18.2

    59 a

    fP

    rimar

    y=

    498.

    33 c

    fs @

    0.

    64 h

    rs,

    Vol

    ume=

    18.2

    59 a

    f, A

    tten=

    0%

    , La

    g= 0

    .0 m

    in

    Prim

    ary

    outfl

    ow =

    Inflo

    w, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -2yr

    Rai

    nfal

    l=2.

    50"

    Nag

    uabo

    Pla

    ya P

    roje

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    age

    10P

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    by C

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    Hyd

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    =20

    3.95

    cfs

    @

    0.72

    hrs

    , V

    olum

    e=5.

    830

    af,

    Dep

    th=

    0.89

    "

    Run

    off b

    y S

    CS

    TR

    -20

    met

    hod,

    UH

    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -2yr

    Rai

    nfal

    l=2.

    50"

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n78

    .710

    80P

    astu

    re/g

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    land

    /rang

    e, G

    ood,

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    G D

    78.7

    10P

    ervi

    ous

    Are

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    .92,

    145

    0.13

    502.

    24La

    g/C

    N M

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    d,

    Con

    tour

    Len

    gth=

    14,

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    t 4S:

    Wes

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    Proj

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    Run

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    =37

    8.86

    cfs

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    0.58

    hrs

    , V

    olum

    e=5.

    038

    af,

    Dep

    th=

    1.18

    "

    Run

    off b

    y S

    CS

    TR

    -20

    met

    hod,

    UH

    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -2yr

    Rai

    nfal

    l=2.

    50"

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n16

    .780

    98P

    aved

    par

    king

    & ro

    ofs

    34.5

    2079

    Woo

    ds/g

    rass

    com

    b., G

    ood,

    HS

    G D

    51.3

    0085

    Wei

    ghte

    d A

    vera

    ge34

    .520

    Per

    viou

    s A

    rea

    16.7

    80Im

    perv

    ious

    Are

    a

    TcLe

    ngth

    Slo

    peV

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    ityC

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    escr

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    n(m

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    (feet

    )(ft

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    )4.

    690

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    500.

    33Sh

    eet F

    low

    , New

    Lan

    dsca

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    : Den

    se

    n= 0

    .240

    P

    2= 5

    .75"

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    500.

    1350

    7.46

    Shal

    low

    Con

    cent

    rate

    d Fl

    ow,

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    ed

    Kv=

    20.

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    62,

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    0.13

    5021

    .84

    38.6

    0C

    ircul

    ar C

    hann

    el (p

    ipe)

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    utle

    tD

    iam

    = 18

    .0"

    Are

    a= 1

    .8 s

    f P

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    = 4.

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    38'

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    .013

    Con

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    ctio

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    32,

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    Tota

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    ino

    Proj

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    ev

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    2.35

    cfs

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    hrs

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    olum

    e=2.

    691

    af,

    Dep

    th=

    1.18

    "

    Run

    off b

    y S

    CS

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    -20

    met

    hod,

    UH

    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -2yr

    Rai

    nfal

    l=2.

    50"

  • Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -2yr

    Rai

    nfal

    l=2.

    50"

    Nag

    uabo

    Pla

    ya P

    roje

    ctP

    age

    11P

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    red

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    arib

    bean

    Hyd

    rolo

    gic

    Eng

    inee

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    2006

    Hyd

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    8

    .00

    s/n

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    309

    2

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    Sof

    twar

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    ions

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    Are

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    escr

    iptio

    n8.

    960

    98P

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    par

    king

    & ro

    ofs

    18.4

    4079

    Woo

    ds/g

    rass

    com

    b., G

    ood,

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    G D

    27.4

    0085

    Wei

    ghte

    d A

    vera

    ge18

    .440

    Per

    viou

    s A

    rea

    8.96

    0Im

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    ious

    Are

    a

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    )4.

    690

    0.13

    500.

    33Sh

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    low

    , New

    Lan

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    peG

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    : Den

    se

    n= 0

    .240

    P

    2= 5

    .75"

    0.1

    500.

    1350

    7.46

    Shal

    low

    Con

    cent

    rate

    d Fl

    ow,

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    ed

    Kv=

    20.

    3 fp

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    62,

    089

    0.13

    5021

    .84

    38.6

    0C

    ircul

    ar C

    hann

    el (p

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    utle

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    = 18

    .0"

    Are

    a= 1

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    = 4.

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    38'

    n= 0

    .013

    Con

    cret

    e pi

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    ends

    & c

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    ctio

    ns6.

    32,

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    Tota

    l

    Subc

    atch

    men

    t 7S:

    Tot

    al C

    lub

    Port

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    o Pr

    ojec

    t Pos

    t Dev

    Run

    off

    =58

    1.28

    cfs

    @

    0.58

    hrs

    , V

    olum

    e=7.

    730

    af,

    Dep

    th=

    1.18

    "

    Run

    off b

    y S

    CS

    TR

    -20

    met

    hod,

    UH

    =SC

    S, T

    ime

    Spa

    n= 0

    .00-

    24.0

    0 hr

    s, d

    t= 0

    .01

    hrs

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -2yr

    Rai

    nfal

    l=2.

    50"

    Are

    a (a

    c)C

    ND

    escr

    iptio

    n25

    .700

    98P

    aved

    par

    king

    & ro

    ofs

    53.0

    1079

    Woo

    ds/g

    rass

    com

    b., G

    ood,

    HS

    G D

    78.7

    1085

    Wei

    ghte

    d A

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    .010

    Per

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    Are

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    n(m

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    )4.

    690

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    500.

    33Sh

    eet F

    low

    , New

    Lan

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    peG

    rass

    : Den

    se

    n= 0

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    P

    2= 5

    .75"

    0.1

    500.

    1350

    7.46

    Shal

    low

    Con

    cent

    rate

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    ow,

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    ed

    Kv=

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    3 fp

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    62,

    089

    0.13

    5021

    .84

    38.6

    0C

    ircul

    ar C

    hann

    el (p

    ipe)

    , Fro

    m C

    urb

    to O

    utle

    tD

    iam

    = 18

    .0"

    Are

    a= 1

    .8 s

    f P

    erim

    = 4.

    7' r

    = 0.

    38'

    n= 0

    .013

    Con

    cret

    e pi

    pe, b

    ends

    & c

    onne

    ctio

    ns6.

    32,

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    Tota

    l

    Pond

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    t Por

    tofin

    o Po

    nd

    Inflo

    w A

    rea

    =51

    .300

    ac,

    Inf

    low

    Dep

    th =

    1.

    18"

    for

    Nag

    1H

    R-2

    yr e

    vent

    Inflo

    w=

    378.

    86 c

    fs @

    0.

    58 h

    rs,

    Vol

    ume=

    5.03

    8 af

    Out

    flow

    =16

    7.48

    cfs

    @

    0.65

    hrs

    , V

    olum

    e=5.

    038

    af,

    Atte

    n= 5

    6%,

    Lag=

    4.5

    min

    Prim

    ary

    =16

    7.48

    cfs

    @

    0.65

    hrs

    , V

    olum

    e=5.

    038

    af

    Rou

    ting

    by S

    tor-

    Ind

    met

    hod,

    Tim

    e S

    pan=

    0.0

    0-24

    .00

    hrs,

    dt=

    0.0

    1 hr

    s

    Type

    II 2

    4-hr

    -15

    min

    .PR

    Tab

    ular

    1.0

    0 hr

    s N

    ag 1

    HR

    -2yr

    Rai

    nfal

    l=2.

    50"

    N