Runoff Hydrographs by dffhrtcv3

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```									RUNOFF HYDROGRAPHS
The Unit Hydrograph Approach
STORM WATER HYDROGRAPHS

   Graphically represent runoff rates vs. time
 Peak runoff rates
 Volume of runoff

   Measured hydrographs are best
   But not often available
   Methods are available to develop a “synthetic” hydrograph
   Use a unit hydrograph (UHG)
DEVELOPMENT OF RO HYDROGRAPHS
 Most often interested in hydrographs at the watershed
outlet (and possibly some selected points in the
watershed).
 We modify the rainfall hyetograph to reflect watershed
characteristics.
 The volume under the effective rainfall hyetograph is
equal to the volume of surface runoff.
HYDROGRAPH COMPONENTS

 qp  is the maximum
flow rate on the
hydrograph
 tp (time to peak) is
the time from the
start of they
hydrograph to qp.
 tb (base time) is the
total time duration of
the hydrograph.
HYDROGRAPH COMPONENTS

 tc (time of concentration) time it takes water to flow
from the hydraulically most remote point in a
watershed to the watershed outlet
 tL (lag time) is the average of the flow times from all
locations in the watershed and can be estimated as
the length of time from the center of mass of the first
effective rainfall block, to the peak of the runoff
hydrograph.
 If each block of effective rainfall has a duration of D

D
t p  tL 
2
UNIT HYDROGRAPH
   Hydrograph of runoff resulting from a unit of
rainfall excess occurring at a uniform rate,
uniformly distributed over a watershed in a
specified duration of time.
UNIT HYDROGRAPHS

   Assumptions:
   Rainfall intensity is not considered
   Linear relationship between stormwater runoff and rainfall
   UHG is independent of antecedent conditions
   Uniform rainfall distribution
DURATION OF THE UNIT HYDROGRAPH
   Each unit hydrograph has a duration that is the
same as the duration of the rainfall excess that
produced it.
 Conceptually can have an infinite # of hydrographs
corresponding to different durations.
 Practically, a unit hydrograph is applied to rainfall
excesses of duration as much as 25% different than
the duration of the unit hydrograph.
HOW IS THE UNIT HYDROGRAPH USED?
   For a unit hydrograph of
duration, D, the volume
underneath the
hydrograph is always 1,
produced by 1 unit of
excess rainfall.
   A hydrograph for a block of
rainfall excess of any
depth is obtained by
multiplying the ordinates
of the unit hydrograph by
the depth of the rainfall
excess block.
    The result is the ordinates
of the runoff hydrograph.
HOW IS THE UNIT HYDROGRAPH USED?

   Rainfall excess is divided into
blocks, each of a uniform
j m
duration, D.
   A component hydrograph for
q j   ri u ji 1
each block of rainfall is               i 1
calculated.
   The starting time for each
hydrograph coincides to the         ri  0 i  m
starting time of the
appropriate block of rainfall
excess.
ui  0 i  n
   All the component
vertically to obtain the total
runoff hydrograph for the
storm.
CHECKING THE VOLUME UNDER A
UNIT HYDROGRAPH.
   Where:
 t is the duration time
increment of the

t  q i         hydrograph (min)

V                 Sqi is the sum of the
ordinates of the runoff
hydrograph (cfs)
60.5A           A is the area (acres)
DERIVING UNIT HYDROGRAPHS
 Unit hydrographs can be derived from
records of observed rainfall and
streamflow
BUT
 For small watersheds, synthetic unit
hydrographs are generally used.
 Synthetic unit hydrographs provide
ordinates of the unit hydrograph as a
function of tp, qp and a mathematical or
empirical shape description.
ESTIMATING THE TIME PARAMETERS
 Time of concentration (tc)
 For some areas, we can sum the time for various
flow segments as the water flows toward the
watershed outlet.
 Segments
 Overland flow
 Shallow channel flow
 Flow in open channels.                 nLi
tc  
i 1 v
i
LAG TIME, TL

SCS Equation to calculate
time lag
L = hydraulic length of
watershed (feet)
S = curve number parameter           L (S  1)
0 .8     0.7
(inches)
Y = average land slope of the
tL          0.5
watershed (%)
1900 Y
tl = time lag (hours)
TIME TO PEAK AND DURATION

 Duration of rainfall
excess should be 1/5 to             D
1/3 tp.                   tp  tL 
 Base time, tb                       2
   tb=2.67 tp.
   Some use tb = 5tp
   Some use tb = ∞
ESTIMATION OF PEAK FLOW PARAMETERS
 General     form                      KA
qp 
tp
 For a triangular unit
hydrograph with                       484 A
tb=2.67 tp                       qp 
tp
 Where:
 tp is the time to peak (hrs)
 qp is peak flow (cfs)
 A is watershed area
(square miles)
SHAPES OF UNIT HYDROGRAPHS
 SCS   uses a dimensionless unit hydrograph
(Figure 3.34).
 Also have a triangular unit hydrograph
derived to have the same tp and qp as the
dimensionless hydrograph.
 If either of these are used the qp and tp are
related through      484 A
qp 
tp
TRIANGULAR HYDROGRAPHS
 Good approximation for peak and duration.
 Find the qp and tp of the unit hydrograph.

 Multiply qp by the depth of the rainfall excess
block.
 Use the tb approximation to find the duration of
the hydrograph.
EXAMPLE 5.10 IN TEXT (MODIFIED)
Solution:
 HSG = D / Commercial  T. 5.1  CN = 95
 S = 0.53 in.

 Assume AMC = II  Q = 1.96 in. of runoff
 Find points to develop the unit hydrograph
 tl = 0.75 hr (45 min)

 tp = 1.25 hr (75 min)

 tb = 3.33 hr (200 min)

 qp = 302 cfs / 1 in. of runoff

 Plot unit hydrograph
 Check area under the triangle  1 in.
600

400
Q (cfs)

qp = 302.5 cfs
300
200

50 tp = 75 100     150   tb = 200
T(min)
Volume under triangle = (302.5 cfs x 4,500 sec) / 2 +
[(302.5 x (12,000 – 4,500 sec)] / 2 = 1,812,000 ft3

Surface runoff depth = 1,812,000 ft3 / 21,780,000 ft2 =
0.08 ft = 1.0 in. ok
EXAMPLE 5.10 IN TEXT
Solution:
qp 2.5” rain = 302.5 cfs x 1.96 in. of SRO
qp 2.5” rain = 592.9 cfs
Plot storm hydrograph
Check area under the triangle  1.96 in.
Q (cfs)
qp = 592.9 cfs
600
Surface runoff depth
= 1.96 in. ok
400
Volume under triangle
300                            = 3,557,400 ft3

200

T(min)
50 tp = 75 100   150   tb = 200
AGSM 335
   Homework #6
SCS DIMENSIONLESS UNIT HYDROGRAPH
   Haan equation                                               1.92
 qptp 
K  6.5
 V   
K
      
q( t )  t 1       t        
 e
tp
        Where:

q(p)  t p
                     

•qp is peak flow (in/hr)
•To convert from cfs to in/hr
divide by A (acres) and
1.008.
•tp is time to peak (hrs)
•V is volume under the
hydrograph (V=1 for unit
hydrograph)
•For a unit hydrograph K should
be close to 3.77
EXAMPLE 5.11 IN TEXT USING SCS UHG
 Rainfall excess for each time block of
duration 15 minutes 0.17, 1.10, 0.84
 tp =52.5 minutes qp = 432 cfs

 Convert qp to in/hr.

 Calculate K

1.92
 q pt p             0.86  .875 
1.92

 V 
K  6.5               6.5                    3.76
                         1      
COORDINATES OF THE UHG
   For each time block of duration D, calculate q(t)
using:                        3.76
 t 1 .875 
t
q(t )        e      432
 .875      
 These are the ordinates of the UHG.
 For each excess rainfall block multiply the depth
of the excess rainfall by all the ordinates of the
unit hydrograph.
 Each hydrograph should begin at the time the
rainfall excess block begins. i.e. If the rainfall
excess block occurred at 30 minutes, the
hydrograph should start at 30 minutes.
CREATING THE TOTAL RUNOFF
HYDROGRAPH
 Add the contents of each row (not including the
UH ordinates) to get the total runoff at each time
t.
 Plot t vs. Q.
UNIT AND RUNOFF HYDROGRAPH
CALCULATIONS
Example of a Unit Hydrograph

qp                               432cfs
K                                3.76
tp                              0.875hr
Excess Runoff (in)
t               q(t)              0.17           0.84              0.71            0.24            Runoff (cfs)
0.00                0.00             0.00                                                                      0.00
0.25               57.04             9.70            0.00                                                      9.70
0.50              263.93            44.87           47.91              0.00                                   92.78
0.75              414.04            70.39          221.70             40.50            0.00                  332.59
1.00              417.11            70.91          347.79            187.39           13.69                  619.79
1.25              329.67            56.04          350.38            293.97           63.34                  763.73
1.50              223.48            37.99          276.92            296.15           99.37                  710.44
1.75              136.27            23.17          187.73            234.07          100.11                  545.07
2.00               76.90            13.07          114.47            158.67           79.12                  365.34
2.25               40.90             6.95           64.59             96.75           53.64                  221.93
2.50               20.76             3.53           34.35             54.60           32.71                  125.18
2.75               10.14             1.72           17.44             29.04           18.45                   66.65
3.00                4.81             0.82            8.52             14.74            9.82                   33.89
3.25                2.22             0.38            4.04              7.20            4.98                   16.60
3.50                1.00             0.17            1.86              3.41            2.43                    7.88
3.75                0.44             0.08            0.84              1.57            1.15                    3.64
4.00                0.19             0.03            0.37              0.71            0.53                    1.65
4.25                0.08             0.01            0.16              0.31            0.24                    0.73
4.50                0.04             0.01            0.07              0.14            0.11                    0.32
4.75                0.01             0.00            0.03              0.06            0.05                    0.14
5.00                0.01             0.00            0.01              0.02            0.02                    0.06
1.00                                                 0.01              0.01            0.01                    0.02
1.25                                                                   0.00            0.00                    0.01
0.00                    0.00
0.00
PLOTS OF UNIT AND RUNOFF
HYDROGRAPHS

Unit and Total Runoff Hydrographs
900.00

800.00

700.00

600.00
Runoff (cfs)

500.00

400.00                                                          Unit Hydrograph
Total Runoff Hydrograph
300.00

200.00

100.00

0.00
0.00   1.00   2.00      3.00      4.00   5.00   6.00
Time (hrs)
BAEN 460
   Homework #6

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