Rational Method

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Surface Drainage/Rational Method

Transverse slope

Longitudinal slope

Longitudinal channel

Surface Drainage System Design

Tradeoffs: Steep slopes provide good hydraulic capacity and lower ROW costs, but reduce safety and increase maintenance costs and erosion

Three phases1. Estimate of the quantity of water to reach the

system2. Hydraulic design of system elements3. Comparison of different materials that serve

same purpose

Hydrologic Analysis: Rational MethodUseful for small, usually urban, watersheds

(<10acres, but DOT says <200acres)

Q = CIA (english) or Q = 0.0028CIA (metric)

Q = runoff (ft3/sec) or (m3/sec)C = coefficient representing ratio of runoff to

rainfallI = intensity of rainfall (in/hour or mm/hour)A = drainage area (acres or hectares)

Iowa DOT Design Manual, Chapter 4, The Rational Method

Runoff Coefficient

• Coefficient that represents the fraction of runoff to rainfall

• Depends on type of surface

Runoff Coefficient

When a drainage area has distinct parts with different coefficients…

Use weighted average

C = C1A1 + C2A2 + ….. + CnAn

Intensity

Average intensity for a selected frequency and duration

Based on “design” event (i.e. 50-year storm) Overdesign is costly (what else?) Underdesign may be inadequate

Duration

Intensity

Based on values of Tc and T Tc = time of concentration T = recurrence interval or design

frequency As a minimum equal to the time of

concentration, tc, (in/hr)

Recurrence Interval (Design Event) 2-year interval -- Design of intakes and

spread of water on pavement for primary highways and city streets

10-year interval -- Design of intakes and spread of water on pavement for freeways and interstate highways

50 - year -- Design of subways (underpasses) and sag vertical curves where storm sewer pipe is the only outlet

100 – year interval -- Major storm check on all projects

Time of Concentration (tc)

Time for water to flow from hydraulically most distant point on the watershed to the point of interest

Assumes peak runoff occurs when I lasts as long or longer than Tc

Depends on: Size and shape of drainage area Type of surface Slope of drainage area Rainfall intensity Whether flow is entirely overland or

whether some is channelized

Ti = L

3600 V

Ti = travel time for section i in watershed (hr)

L = flow length (ft)

V = average velocity (ft/sec)

Tc: Equation from Iowa DOT Manual

(See nomograph)

Nomograph Method

Trial and error Estimate I Determine Tc

Check I and Tc against values in Table 5 (Iowa DOT, Chapter 4)

Repeat until I ~ Tc

Example (Iowa DOT Method)

Iterative finding I and Tc

L = 150 feet Average slope, S = 0.02 Grass Recurrence interval, T = 10 years Location: Keokuk Find I

From Iowa DOT Design Manual

Grass Surface, mannings roughness coefficient = 0.4

Try I = 5 in/hr

Tc = 18 min

Example (continued)

Tc with first iteration is 18 min Check against tables in DOT manual

Keokuk is in SE, code = 9

Convert intensity to inches/hour

From previous chart:

6.32 inches occurs over 5 days (120 hours) =

6.32 in/120 hours = 0.05 in/hr

4.06 inches occurs over 18 hours =

4.06 in/18 hours = 0.34 in/hr

1.26 inches occurs over 15 min =1.26 in/0.25 hours = 5.0 in/hr

For intensity of 5 inch/hr, Duration is 15 min

Tc from nomograph was 18 min

Example (continued)

I < Tc

Next iteration, try intensity = 4.0 inch/hr

Slope = 0.02

I = 4.25 inches/hr

Tc = 20 min For second iteration, tc = 20 min,

Example (continued)

I < Tc

Next iteration, try intensity = 4.25 inch/hr

I = 4.25 inches/hour is somewhere between 30 min and 15 min

Example (continued)

I = 4 inches/hour is somewhere between 30 min and 15 min

Example (continued)

Interpolate

I at 20 min = 4.3 inches/hour

Close so I = 4.25 inches/hour

Area of watershed Defined by topography Use ArcView contours in lab

Q = CIA

Calculate once C, I, and A have been found

Rational Method

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