calculating detention basin volume - graphical storage method

Calculating Detention Basin Volume - Graphical Storage Method

Procedure

tep 1: Determine the allowable peak release rate (Qo) for the basin in cfs (cubic feet per second) or csm(cubic feet per second per square mile.)

The most common procedure used to determine Qo is to limit the downstream discharge rate to thepre-development discharge rate for the selected design storm. This rate can be determined using theGraphical Peak Discharge Method or the Tabular Hydrograph Method.

Step 2: Calculate the peak inflow rate (Qi) for the developed conditions in the same units used for Qo.

This rate can also be determined using the Graphical Peak Discharge Method or the TabularHydrograph Method.

Step 3: Calculate the ratio Qo/Qi of design release rate (Qo) to the inflow rate (Qi) in the same units.

Step 4: Using Diagram 10, enter the graph with Qo/Qi; move vertically to intersect the curve; then movehorizontally to read the value for the ratio Vs/Vr.

Step 5: Calculate the required storage volume (Vs) in watershed inches by multiplying the Vs/Vr ratio bythe volume of runoff (Vr) in inches for the "developed" condition.

Step 6: Convert Vs from watershed-in. to acre-ft. by multiplying Vs (inches) by the watershed area(acres) and dividing by 12 in./ft.

Step 7: Proportion the storage basin and design the discharge structure so that the allowable release rateis not exceeded and the maximum water storage elevation is known. This requires the development of anelevation-storage curve for the basin and an elevation-discharge curve for the proposed outlet structures. The objective is to select an outlet structure which will discharge at the allowable release rate when thewater reaches the maximum storage elevation. We will end our calculations with Step 6.

Example 1

Calculating Detention Basin Volume - Graphical Storage Method http://water.me.vccs.edu/math/graphsm.htm

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A developer proposes to construct a residential subdivision on a 75-acre tract of woodland. The 75-acretract is the entire drainage area of a main channel which intersects a natural stream at the propertyboundary. The developer is required to detain stormwater in a basin to be constructed on the mainchannel below the development so that the peak rate of runoff entering the natural stream afterdevelopment does not exceed the pre-development peak runoff rate for a 2-year frequency design storm. This example uses the Type II storm distribution since the project is located in south-central Virginia.

The following information is given. Rainfall depth listed refers to a 2-year storm.

Drainage area(acres)

F-value CN Rainfalldepth (in.)

Tc

(hours)

Pre-development

75 1 60 4.5 0.70

Post-development

75 1 75 4.5 0.75

Find: The required storage volume of the basin.

Step 1: Determine the allowable release rate, Qo.

In order to determine the allowable release rate, you need to determine the peak flow rate for thepre-development area during a 2-year storm. We will need to know the runoff depth for a later step,so we will calculate it here as well. We have used the Peak Discharge Method and the giveninformation to calculate these values. The calculations are not given - you should attempt thesecalculations on your own.

Calculated values:Peak discharge = 35 cfsRunoff depth = 1 inch

The allowable release rate, Qo, is the runoff depth from the 2-year storm, which is 35 cfs.


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Step 2: Calculate the peak inflow rate (Qi) for the developed conditions.

We can determine Qi using the Peak Discharge Method on the post-development area during a2-year storm.

Calculated values:Peak discharge = 90 cfsRunoff depth = 2 inches

The peak inflow rate, Qi, is the runoff depth, which is 90 cfs.

Step 3: Determine Qo/Qi.

Step 4: From Diagram 10, determine Vs/Vr.

Enter the curve at the bottom, at a value of 0.389. Intersect the curve for Types II and III, and gohorizontally to the Vs/Vr ratio.

The value for Vs/Vr based on Diagram 10 is approximately 0.326.

Step 5: Calculate the required storage volume, Vs.

We have already calculated the Vr value - this is the runoff depth for the post-developed watershedduring the 2-year storm. From step 2, the Vr value for this watershed is 2 inches.

To calculate the storage volume, use the following equation:

In the case of our example, the storage volume is:


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Step 6: Convert Vs to acre-feet.

To convert the storage volume to acre-feet, use the following equation:

In the case of our example, the storage volume translates to:

Example 2

The watershed illustrated below is to be developed according to a predetermined plan. Subareas 4 and 6will be developed while the other subareas will be left in pre-development condition.

In order to contain the extra runoff resulting from development of subareas 4 and 6, a detention basin isplanned for the base of each developed subarea.

Given:

The post-development tabular hydrograph is shown below. (This tabular hydrograph was developedusing the method explained in Lesson 10. The discharge values found using Table 13 wereconverted from csm/in. to cfs by multiplying the csm/in. discharge value by the watershed area.)

Time (in hours)


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13.213.413.613.814.0(Sub) Area Name Discharge (cfs)Entire Watershed 316 323 335 316 291Subarea 4 2 9 23 41 55Subarea 6 140 136 131 101 77

The Ia/P, Tc, Vr, and drainage area of subareas 4 and 6 are shown in the table below.

Subarea Ia/P Tc Vr *Drainagearea

4 0.10 0.75hrs.

1.01in.

0.25 mi.2

6 0.10 1.50hrs.

1.30in.

0.40 mi.2

The allowable peak release rate for the entire watershed is 230 cfs.

Find: The peak release rates and required storage volumes for stormwater detention basins located at theoutlets of subareas 4 and 6 so that the composite peak discharge rate at the outlet of subarea 7 will notincrease after development for the selected design storm.

First: Determine the combined allowable release rate for the detention basins in subareas 4 and 6.

The discharge values which will be contributed by subareas 4 and 6 are subtracted from thedischarge values for the entire watershed, as shown below:

Time (in hours) 13.213.413.613.814.0

(Sub) Area Name Discharge (cfs)Entire Watershed 316 323 335 316 291Subarea 4 2 9 23 41 55Subarea 6 140 136 131 101 77Entire Watershed minus Subareas 4 & 6: 174 178 181 174 159

The post-development peak discharge, discounting the contribution from subareas 4 and 6, is shownto be 181 cfs based on the table above. We will call this value the partial discharge.

Using the partial discharge calculated above and the given allowable peak release rate for thewatershed, we can determine the allowable release rate for the two subareas in question using thefollowing formula:

Subarea discharge = Watershed discharge - Partial discharge

In the case of our example, the calculation is as follows:

Subarea discharge = 230 cfs - 181 cfs

Subarea discharge = 49 cfs


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Therefore, subareas 4 and 6, combined, can release 49 cfs of water from their detention basins.

Second: Choose suitable detention basin volumes.

It is now necessary to decide the distribution of the 49 cfs release rate between the two detentionbasins. To do so, we choose a release rate for one detention basin and use the following formula tofind the release rate of the other detention basin:

Basin A discharge = Subarea discharge - Basin B discharge

We will start with an assumed release rate of 30 cfs for the detention basin at the outlet of subarea 6(structure 6A.) Then we can calculate the release rate of structure 4A to be:

Structure 4A = 49 cfs - 30 cfs

Structure 4A = 19 cfs

Now we just have to calculate the required storage volume for each detention basin using themethod explained earlier in this lesson. The next two steps show how to determine the storagevolume of structures 4A and 6A.

Third: Determine Storage Volume of Structure 6A

The peak release rate, Qo, is given to be 30 cfs. 1.

Qi must be calculated separately from the peak value given for subarea 6 in the composite tabularhydrograph (140 cfs in the case of this example.) The value on the composite tabular hydrographrepresents the subarea's contribution to the runoff at the outlet of subarea 7, while the value weneed is the peak discharge at the outlet of subarea 6. The steps used to determine Qi for subarea 6are shown below:

2.

Read the tabular hydrograph unit discharge (Qt) off Table 13. (Values have been given forIa/P and Tc. When using a tabular hydrograph to estimate Qi for a subarea of a watershed, Tt

is always set equal to 0.) In our example, Qt = 275 csm/in.

Calculate Qi using the following equation:

Qi = Qt Am Vr

Where:Qi = Peak inflow rate (cfs)Qt = Tabular hydrograph unit discharge (csm/in.)

Am = Drainage area (mi.2)Vr = Total runoff (in.)

In the case of our example, values for Am and Vr have been given. Qi is determined using thefollowing calculations:

Qi = (275 csm/in.) (0.4 mi.2) (1.30 in.)


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Qi = 143 cfs

Qo/Qi is calculated as is shown below:

3.

From Diagram 10:4.

Since it is given that Vr = 1.30 in., the storage volume of the detention basin is:5.

We can convert the storage volume to acre-feet as follows:

6.

Fourth: Determine Storage Volume of Structure 4A

1. The peak release rate, Qo, is given to be 19 cfs. 2. Qi is calculated to be 107 cfs using the given information and the method explained under thecalculations for Structure 6A.

3. Qo/Qi is calculated to be 0.18.

4. From Diagram 10:

5. Since it is given that Vr = 1.01 in., the storage volume of the detention basin is 0.47 in.

6. We can convert the storage volume to 6.3 acre-feet.

ConclusionsUsing the peak release rates of 19 cfs and 30 cfs for structures 4A and 6A, respectively, the storagevolume of the basins must be 6.3 acre-feet for structure 4A and 12.6 acre-feet for structure 6A. Othertrial calculations could be made to determine the most economical allocation of storage between the twodetention basins. Then the structures could be designed using storage curves for the impoundment sitesand elevation-discharge curves for the selected discharge structures.


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Designing a Detention Basin

Once the volume of a detention basin has been determined, the detention basin can be designed using thefollowing steps.

Step 1: The required volume is translated to cubic feet.

Step 2: A depth is chosen. Using this depth, surface area is calculated using the following equation:

Volume = Depth c Surface Area

Step 3: By choosing a rectangular shape, the length and width calculations are simplified. A length ischosen and the width is determined using the following equation:

Surface Area = Length × Width

Step 4: Now the detention basin can be designed, taking into account the following requirements:

20 ft. wide vegetated buffer.At least 20 ft. from any property line.At least 100 ft. from any septic tank/drain field.At least 50 ft. from any steep slope (greater than 15%.)Side slopes less steep than 3H:1V.An aquatic bench when surface area exceeds 20,000 square feet.

Example

Step 1: 9.4 acre-ft. × (43,560 ft.2/1 acre) = 409,464 ft.3

Step 2: A depth of 1.5 feet is chosen since this depth will allow the growth of aquatic vegetation. Usingthis depth, the surface area can be calculated as follows:

409,464 ft.3 = 1.5 ft. × Surface Area

272,976 ft.2 = Surface Area

Step 3: Choosing a length of 740 feet results in a width of 369 feet as shown below:

272,976 ft.2 = 740 ft. × Width

369 ft. = Width

Step 4: The detention basin is designed as follows:


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calculating detention basin volume - graphical storage method

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