:ak flow estimation that uses

;t peak flows for a rainfallwer design because this typethe simplicity of the

3that a steady state isinagebasin is equal to thelumetric inflow rate as the

y ie, the outflow rate Q is;, the effective intensity is ait, resulting in

;calculations by handit the discharge Q is in unitsn units of m3/s.

entire basin is contributingbe at least as long as the time. Also, steady-statemporally uniform. It is notiqx a large drainage basin, orlong as the time ofe conditions limit the

s. An upper limit of 200 acres;nd on the storm

istics may limit the0 acres in some cases.

:ommon facility such as aaken as the longest of all theavel times when appropriate,dualbasin areas) should bee) of the Rational Method.

)ws:

Basic Hydrology Chapter 2

Step 1:Apply I-D-F DataDevelop or obtain a set of intensity-duration-frequency (IDF) curves for the locale inwhich the drainage basin resides. Assume that the storm duration is equal to the time ofconcentration and determine the corresponding intensity for the recurrence interval ofinterest. Note that the assumption that the storm duration and time of concentration areequal is conservative in that it represents the highest intensity for which the entiredrainage area can contribute.

Step 2: Compute Watershed Area

The basin area A can be estimated using topographic maps, computer tools such as CADor GIS software, or by field reconnaissance. The time of concentration may be estimatedusing the procedures discussed in the preceding subsection.

Step 3: Choose C Coefficients

The runoff coefficient Cmay be estimated using Table 2-5 if the land use ishomogeneous in the basin, or a composite C value may be estimated if the land use isheterogeneous (see Example 2-6).

Step 4: Solve Peak Flow

Finally, the peak runoff rate from the basin can be computed using the equation Q

The following example illustrates the use of the Rational Method for several subbasinsdraining into a common storm sewer system.

CiA.

Example 2-9: Computing Flows for Multiple Subbasins with the Rational Method

Figure 2-13 is a plan view of a storm sewer system draining three subbasins. Use theRational Method to determine the peakdischarge in eachpipe and size eachpipeassuming the pipes flow full. Assume also that the pipes will be concrete with n = 0.013.Perform the calculations for a storm recurrence interval of 25 years. Subbasin and pipecharacteristics and IDF data for the 25-year event are tabulated as follows:

Subbasin A{ac) C tc (min)

A 6.0 0.6 20B 4.0 0.8 10

C 4.5 0.8 15

Pipe Length (ft) Slope (%)1 500 1.0

2

3

400

500

1.2

0.9

61

Computer Applications in Hydraulic Engineering

Duration (min) Intensity (in/hr)

5

10

8.40

7.02

15 5.96

20

30

5.26

4.42

60 2.97

Subbasin A

Subbasin B

0

To Outfall

Figure 2-13: System for Example 2-9

62

Subbasin C

Pipe 2-n

BasicHydrology Chapter 2

Solution

Flow into Pipe 1 occurs from Subbasin A only. Using the time of concentration as thestorm duration, the 25-year rainfall intensity is 5.26 in/hr. The peak discharge used insizing Pipe 1 is therefore

Q = 0.6(5.26)(6.0)= 19 cfs

Assuming that Pipe 1 is flowing full, its required diameter D may be found usingManning's equation as follows:

D =Qn

0.464S1

19(0.013)

0.464(0.01)"= 1.87 ft A"

Rounding up to the next commercially available size, Pipe 1 should have a diameter of 24inches. Use FlowMaster to determine that the depth of flow is 1.40 ft and the area of flowis 2.36 ft". flo^j

Because the cross-sectional area ofPipe 1 is 2.36 ft2, the average velocity inPipe 1 is

V= QlA =191236 = 8.05 ft/s

The travel time in Pipe 1 is

t = LIV= 500/8.05 = 62 s = 1.04 minutes

Pipe 2 is treated the same way as Pipe 1, recognizing that runoff from Subbasin C onlyenters Pipe 2. The peak discharge from Subbasin C is Q = 22 cfs, and the requireddiameter of Pipe 2 is D = 24 in. The travel time in Pipe 2 is t = 45 s = 0.75 min.

Pipe 3 must be sized to handle the runoff from all three of the subbasins, which have atotal area of A = 14.5 acres. The runoff coefficient for the combined areas is computed asa composite value and is

c_ 6(0.6)+ 4(0.8) +4.5(0.8) _Q7214.5

The time of concentrationis computedas the longest of the travel times to the upstreamend of Pipe 3. These travel times are (1) the time of concentration of Subbasin B (10minutes), (2) the time of concentration of Subbasin A plus the travel time in pipe 1 (20 +1.0 = 21 min), and (3) the time of concentration of Subbasin C plus the travel time inPipe 2 (15 + 0.75 = 15.75min). Thus, the time of concentration for Pipe 3 is 21 minutes,and the corresponding rainfall intensity (by interpolation) is 5.17 in/hr.

The peak discharge for Pipe 3 is

e = 0.72(5.17)(14.5) = 54cfs

The required diameterof Pipe 3 (rounded to the nearest standard size) is 36 inches.

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63

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APPENDIX 19.CCircular Channel Ratios'2'6

APPENDICES A-39

Experiments have shown that n varies slightly with depth. This figure gives velocity and flow rate ratios for varyingn (solid line) and constant n (broken line) assumptions.

1.0 1.2 1.4 1.6

values of -i- and —'full "fu

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

(D ^-0*

0-1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

JL _y_ A 1Qull vfull Aull "full

Governing equations

1.1 1.2 1.3

hydraulic elements ~, — , -^-, ~ , and —"full

aMu" °'» ®

If-'lD I9deg = 2 arccos

2 /

,4 =/D\2flrad-sin8degl2i 2

P = OBrad2

R =A

|lǤ)r?K

Slope is constant.

n = 0.013

"fun " \di \dI

"Adapted from Design and Construction of Sanitary and Storm Sewers, p. 87, ASCE, 1969, as originally presented in "Design of Sewers^o Facilitate Flow.' Camp, T. R., Sewage Works Journal, 18. 3 (1946)

'or n = 0.013

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