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Hydrologic Analysis

By Michael J. Mastroluca P.E.

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Chapter 3 Objectives

Define the concept of a watershed

Discuss quantification of watershed, soil,

and channel characteristics

Provide and understanding of the

importance of watershed characteristics in

controlling flood runoff

Discuss simplifying assumptions made incharacterizing flood runoff

Characterize the timing of flood runoff

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Watershed Characteristics

Watershed characteristics that affect thehydrologic cycle : (see notes for explanation)

each area will be discussed in detail

Size of drainage area

Slope, length

Land use

Soil type

Storage and vegetation in channel Channel roughness and cross-sectional properties

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What is a Watershed?

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Answer

According to the EPA a watershed is an area of land that

catches rain and snow and drains or seeps into a marsh,

stream, river, lake or groundwater

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Delineation of a watershed

1. Hand drawn on a paper

topographic map

2. Contour line (Continuous

line for the same

elevation points) use

3. Requires experience and

labor

4. Analogue approach

5. Manual

Outlet point

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Example Problems

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Chapter 3 handout

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Open Channel Flow

1. Uniform flow - Mannings Eqn in a prismatic

channel - Q, v, y, A, P, B, S and roughness are all

constant

2. Critical flow - Specific Energy Eqn (Froude No.)

3. Non-uniform flow - gradually varied flow (steady

flow) - determination of floodplains

4. Unsteady and Non-uniform flow - flood waves

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Mannings Equation

Cross-Section

Profile

Wetted Perimeter

Area

BedSlope

Roughness

QAR S

n

h

1492

31

2.

Q = Flow

A=

Cross-sectional areaRh = Hydraulic Radius (area/wetted perimeter)

S = Bed slope

n = Roughness coefficient

Unlined Open Channels Mannings n range

A. Earth, uniform section:

A.1. Clean, recently completed 0.016 - 0.018A.2. Clean, after weathering 0.018 - 0.020

A.3. With short grass, few weeds 0.022 - 0.027

A.4. In gravely soil, uniform section, clean 0.022 - 0.025

B. Earth, fairly uniform section:

B.1. No vegetation 0.022 - 0.025

B.2. Grass, some weeds 0.025 - 0.030

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Concrete Channel

Uniform Open Channel Flow

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Normal depth is function of flow rate, and

geometry and slope. One usually solves for normal

depth or width given flow rate and slope

information

B

b

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Normal depth implies that flow rate, velocity, depth,

bottom slope, area, top width, and roughness remain

constant within a prismatic channel as shown below

Q = C

V = C

y = C

S0 = CA = C

B = C

n = C

UNIFORM FLOW

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a

z

1

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Optimal Channels - Max R and Min P

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Uniform FlowEnergy slope = Bed slope or dH/dx = dz/dx

Water surface slope = Bed slope = dy/dz = dz/dx

Velocity and depth remain constant with x

H = z + y + av2/2g = Total Energy

E = y + av2/2g = Specific Energy

a often near 1.0 for most channels

H

a = S vi2 Qi

V2 QT

Energy Coeff.

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Critical depthis used to characterize channel flows -

based on addressing specific energyE = y + v2/2g orE = y + Q2/2gA2

where Q/A = q/y and q = Q/b

Take dE/dy = (1 q2/g y3) and set= 0. q= const

E = y + q2/2gy2y

E

Min E Condition, q = C

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Solving dE/dy = (1 q2/g y3) and set= 0.

For a rectangular channel bottom width b,

1. Emin= 3/2Yc for critical depth y = yc

2. yc/2 = Vc2/2g

3. yc = (Q2/gb2)1/3

Froude No. = v/(gy)1/2We use the Froude No. to characterize critical flows

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Y vs E E = y + q2/2gy2q = const

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In general for any channel shape, B = top width

(Q2/g) = (A3/B) at y = yc

Finally Fr = v/(gy)1/2 = Froude No.

Fr = 1 for critical flow

Fr < 1 for subcritical flow

Fr > 1 for supercritical flow

Critical Flow in Open Channels

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Example Problems

Calculate the depth of water and the velocityfor two trapezoidal channels:

Concrete lined

Bottom width is 3 ft Slopes

2%

6%

Side slopes 2 to 1

Discharge of 30 cfs

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Example Problem

Compute By Hand

Compute using Visurban

Compute using nomograph Compute using Flow Master

How do your answers compare to each other? Which channel is flowing super critical?

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Travel Time

In summary, the velocity method is the common

method of computing time of concentration using

in TR-55 and TR-20.

Velocity Method (Overland, shallow concentrated andchannel or pipe flow)

Travel Time (Tt) = L (length) / V (velocity)

(Equation 3-43)

Tc = summation of travel time for each flow segment

Other methods are available (empirical), Nomographs

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Travel Time (cont) Overland Flow

Refer to as sheet flow

Occurs within the first 300 feet

In Equation 3-3, which is the SCS Kinematic Wave Equation

P is the 2-Year- 24 hour Precipitation

Shallow Concentrated Flow Occurs after 300 feet Calculated using equation 3-1

and Figure 3-1

Channel Flow or Pipe Flow

First use Manning's Equation to calculate velocity and then plug Vinto Equation 3-1 to get time.

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Sheet Flow < 300 feet

]33.[)(

)(007.04.05.0

2

8.0

eqsP

nL

Tt

)/(

)(24,2

)(

)13('

)(

:

2

f tf tslopelandlinegradehydraulicofslopes

infallrainhouryearP

f tlengthflowL

tabletcoefficienroughnesssManningn

hrtimetravelT

where

t

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Computing TtShallow Concentrated Flow

]13.[600,3

eqV

L

Tt

hourstoecondsforfactorconversion

sf tvelocityaverageVf tlengthflowL

hrtimetravelTt

s600,3

)/()(

)(

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Figure 3-1 Velocity

Average Velocity

Figure 3-1

Appendix F

For slopes < 0.005

Calculate Tt with Eq. 3-1

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Shallow Concentrated Flow (cont.)

Appendix F (slope < 0.005)

5.0

5.0

)(3282.20

)(1345.16

sVPaved

sVUnpaved

)/,(

)/(:

f tf tslopeewatercours

gradelinehydraulicofslopes

sf tvelocityaverageVwhere

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Manning's Equation

Open Channel Flow

]43.[49.1 2

1

3

2

eqn

srV

tcoefficienroughnesssManningn

ftf tslopechannelgradelinehydraulictheofslopes

ftperimeterwettedp

ftareaf lowectionalscrossa

paf tradiushydraulicr

w

w

'

)/,(

)(

)(

)(

2

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GivenHartford County, CT

2-Yr, 24-Hr rainfall = 3.6A-B: Sheet flow, dense grass, s=0.01, L=100

B-C: Shallow concentrated flow, unpaved, s=0.01,L=1400C-D: Channel flow, n=0.05, a=27ft2,pw=28.2,s=0.005, L=7300

FindTc at D

Example

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Travel Time (cont)

Examples Use TR55 spreadsheet Use TR55 Program

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National Resource Conservation Service (NRCS)

Curve Number (CN) Concepts

Curve number of an indicates the runoff potential

of the area (see table 3.18)

1) Antecedent moisture:

Is based upon rainfall during that occurred five dayspreceding the storm

a. AMC I (dry): little rainfall preceding the rainfall in question

b. AMC II (average):

1.4-2.1 inches of rainfall during the previous 5 days duringgrowing season

0.5-1.1 inches of rainfall during previous 5 days during dormant

season

c. AMC III (wet): considerable rainfall prior to the rain in

question

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CN cont.

Changes in AMC are reflected through changes in theCurve Number

Curve numbers given are for AMC II, which is based onmedian values for CN taken from sample rainfall and

runoff data Curve numbers for antecedent conditions I or III can be

estimated using: Table 3-19

2) Hydrologic Soil Group: see table 3-17

3) Land use: Land use coefficients are available fora large number of land uses and conditions. Seetable 3-18

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Weighted CN

i

ii

A

CNA

CNw=

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NRCS Curve Number Method

Uses

Typically used in TR-55, TR-20, HEC-1 and HMS

Spread sheet available on Black Board

On your free time please download the

program and manual from NRCS. It will be

needed in the future

http://www.wcc.nrcs.usda.gov/hydro/hydro-tools-

models-tr55.html

QP S

P S

0 2

08

2.[eq. 2-3]

http://www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.htmlhttp://www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.htmlhttp://www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.htmlhttp://www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.htmlhttp://www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.htmlhttp://www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.htmlhttp://www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.htmlhttp://www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.htmlhttp://www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.html

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Q

P S 08.[ q ]

SCN

100010 [eq. 2-4]

Q = Runoff (in.)

P = Rainfall (in.)

S = Potential maximum retention after runoff begins (in.)CN = SCS Runoff Curve Number

Primary

Equations and

Curve

Numbers

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CN Examples

Use TR-55

Use TR-55 Spread sheet

Use TR-55 program