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2015 PE Review: Hydrology and Hydraulics

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2015 PE Review: Hydrology and Hydraulics Michael C. Hirschi, PhD, PE, CPESC, D.WRE Senior Engineer Waterborne Environmental, Inc. hirschim_at_waterborne-env.com – PowerPoint PPT presentation

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Title: 2015 PE Review: Hydrology and Hydraulics


1
2015 PE ReviewHydrology and Hydraulics
  • Michael C. Hirschi, PhD, PE, CPESC, D.WRE
  • Senior Engineer
  • Waterborne Environmental, Inc.
  • hirschim_at_waterborne-env.com
  • also Professor Emeritus
  • University of Illinois

2
Acknowledgements Daniel Yoder, I-A, PE Review
2006 Rafael (Rafa) Muñoz-Carpena, I-A, PE Review
2007-09 Rod Huffman, past PE Review coordinator
3
Session Topics
  • Hydrology
  • Hydraulics of Structures
  • Open Channel Flow

4
Hydrology
  • Hydrologic Cycle
  • Precipitation
  • Average over Area
  • Return Period
  • Abstractions from Rainfall
  • Runoff
  • Hydrographs
  • Determination methods

5
Hydraulics of Structures
  • Weir flow
  • Orifice flow
  • Pipe flow
  • Spillway flow
  • Stage-Discharge relationship

6
Open Channel Flow
  • Channel geometries
  • Triangular
  • Trapezoid
  • Parabolic
  • Mannings equation
  • Manning roughness, n
  • Grass waterway design

7
A few comments
  • Material outlined is about 3 weeks or more in a
    3-semester hour class. Im compressing at least
    6 hours of lecture and 3 laboratories into 2
    hours, so I will
  • Review highlights and critical points
  • Do example problems
  • You need to
  • Review and tab references
  • Do additional example problems, or at least
    thoroughly review examples in references

8
Hydrologic Cycle
From Fangmeier et al. (2006)
9
Precipitation
  • Input to the Rainfall-Runoff process
  • Forms include
  • Rainfall
  • Snow
  • Hail
  • Sleet
  • Measured directly
  • Varies temporally and areally

10
Rainfall Data
  • Daily
  • Hourly
  • 15-minute
  • Continuous
  • Reported as depth, which is really volume over a
    given area, over a period of time

11
Average Rainfall
  • Simple arithmetic average
  • Theissen Polygon

12
Example 1
  • How do different calculation methods of rainfall
    average compare?
  • Consider

13
Raingage data
  • Gages (clockwise from upper left) 1.9, 2.1,
    1.8, 1.9, 2.1, 2.2
  • Arithmetic average 2.0

14
Theissen Polygons
  • Areas closest to each raingage determined by
    perpendicular bisectors of each line between
    raingages.
  • Areas for each raingage, again clockwise from
    upper left 65ac, 150ac, 55ac, 140ac, 215 ac,
    270ac
  • Figure is repeated with Theissen polygon
    construction added.

15
Why bisectors?
  • When perpendicular bisectors are constructed,
    they are, by definition, lines that are
    equidistant from the points at the ends of the
    lines they bisect.
  • So, the combination of the constructions
    delineate areas that are closest to a given point
    (raingage in this case)

16
  • Is the watershed average
  • rainfall using the Theissen
  • Polygon method most nearly
  • 2.0
  • 2.1
  • 2.2
  • 1.9

17
Theissen calculation
  • Uses areal weighted average, so the sum of the
    products of area x depth divided by total area
  • Hint If you measure the areas yourself, the
    denominator should be the sum of the areas, not
    the known watershed area
  • So, average Theissen rain Answer B, 2.1
  • (651.91502.1551.81401.92152.12702.2)/(6
    515055140215270)2.07, which is best
    represented as 2.1 given most data is 2
    significant digits.

18
Any questions on Theissen Polygons?
19
Return Period (two descriptions)
  • A 10 year-24 hour rainfall volume is that depth
    of rainfall over a 24 hour period that is met or
    exceeded, on the long-term average, once every 10
    years.
  • Another way to describe it is the 24 hour
    rainfall depth that has a 1 in 10 (10) chance to
    be met or exceeded each year, on the long term
    average.

20
US 100yr-24hr Rainfall
100yr-24hr data from TP-40 (Hershfield (1961) as
referenced by Fangmeier et al. (2006)
21
Return Period Data
  • Constructed from historical rainfall data
  • Available in tabular form via website or state
    USDA-NRCS reports.
  • Available as national maps (similar to previous
    slide) in several references such as Haan,
    Barfield Hayes (1994).

22
Example
  • A reservoir is to be designed to contain the
    runoff from a 10yr-24hr rainfall event in
    Northeastern Illinois. What rainfall volume is
    to be considered?
  • 4.5
  • 3.9
  • 4.1
  • Cannot estimate from available maps

23
10yr-24hr map from Haan, Barfield Hayes (1994)
24
Example
  • Answer is C. From map, 10yr-24hr rainfall in NE
    Illinois is just over 4, use 4.1 to be
    conservative.

25
Questions on precipitation?
26
Abstractions from Rainfall
  • Abstractions from rainfall are losses from
    rainfall that do not show up as storm water
    runoff
  • Interception
  • Evapotranspiration
  • Storage
  • In bank
  • On surface
  • Infiltration

27
Runoff by other names
  • Effective rainfall
  • Rainfall excess

28
Runoff
  • If rainfall rate exceeds the soil infiltration
    capacity, ponding begins, and any soil surface
    roughness creates storage on the surface. After
    at least some of those depressions are filled
    with water, runoff begins. Additional rain
    continues to fill depressional storage and runoff
    rate increases as more of the hill slope and
    subsequently the watershed contributes runoff.

29
Rainfall/Runoff process
30
Time of Concentration, tc
  • The time from the beginning of runoff to the time
    at which the entire watershed is contributing
    runoff that reaches the watershed outlet is
    called the Time of Concentration. It is also
    described as the travel time from the
    hydraulically most remote point in a watershed to
    the outlet.

31
Curve Number method
32
CN Method, continued
33
Time of Concentration, tc
34
CN values
35
Runoff Volume determination
36
Runoff Example
  • In a previous problem, a design rain event in NE
    Illinois was determined to be 4.1. Assuming the
    watershed in question was a completed 300 ac
    residential area with an average lot size of ½
    ac, all on Hydrologic Group C soils, what is the
    needed pond volume, if all runoff is to be
    retained?
  • A 2.5 runoff-inches
  • B 53 acre-inches
  • C 630 acre-ft
  • D 53 acre-ft

37
Runoff Example, continued
38
Runoff Volume determination
39
Answer to Runoff Example
  • The answer is D, 53 acre-ft. From the table, the
    CN for Hyd group C soil with ½-ac lot is 80.
    Using the graph with a 4.1 rainfall, runoff
    depth is 2.1. Volume is then 300ac2.1in 630
    ac-in, divided by 12 is 53 ac-ft.

40
Additional example
  • You discover that the subdivision is actually 100
    acres of ½ ac lots on C soils, 100 acres of ½ ac
    lots on D soils, 50 acres of ¼ ac lots on B soils
    and 50 acres of townhouses on A soils. What CN
    value would you use?
  • A 79
  • B 85
  • C 80
  • D 75

41
Addl Runoff Example, cont.
42
Answer
  • The correct answer is C, 80. Use an
    area-weighted average, similar to Theissen
    method. The respective CN values for ½ ac on C,
    ½ ac on D, ¼ ac on B and townhouses on A are 80,
    85, 75 77. The area-weighted CN is then
    (801008510075507750)/300 80.33, which is
    more appropriately 80.

43
Peak Discharge
  • The CN method also provides for Peak Discharge
    estimation, using graphs or tables. Required
    information includes average watershed slope,
    watershed flow path length, CN, and rainfall
    depth. The graphical method from the EFM is

44
Peak Runoff Discharge
45
Peak Discharge Example
  • Same residential watershed that produced 2.1 of
    runoff from a 4.1 rainfall. Flow length is
    2500, slope is 2. CN is 80, so S is 2.5. Ia
    0.2S 0.5. Ia/P 0.5/4.10.122.
  • Tc 25000.8(1000/80-9)0.7/1140/20.5
  • 0.8hr

46
Peak Runoff Discharge
47
Example solution
  • From graph, with Ia/P of 0.122 and Tc of 0.8hr,
    unit peak discharge is 0.57 cfs/ac/in or qp
    0.573002.1 360 cfs

48
Rational Method
  • The Rational Equation is

Qp CiA where C is a coefficient i is rainfall
intensity of duration tc A is area in acres
C is approximately 0.4, A is 300ac, i is 2 in
30min, so 4iph, peak rate is then 0.43004 480
cfs
49
Questions on runoff?
50
Hydraulics of Structures
  • Flow through structures is important given that
    such structures control the rate of flow. Sizing
    of such structures is then important to allow
    flow to pass while protecting downstream areas
    from the effects of too high a flow rate.
    Structures may also be used for measurement of
    water flow. Each type of structure will produce
    different types of flow depending upon size and
    flow rate passing through it.

51
Weirs
  • Sharp-crested
  • Broad-crested

52
Weir Equation
(from EFH-Ch03 Hydraulics)
53
Sharp-Crested Weir
(from EFH-Ch03 Hydraulics)
54
More complex weirs(from Haan et al., 1994)
55
Example
  • You are measuring flow using a 90 V-notch weir.
    H is measured as 0.53 at 2.5 upstream of the
    weir. What is the flow rate?
  • 230 gpm
  • B. 0.51 cfs
  • C. 0.51 gpm
  • D. A B

56
Answer
  • The answer is D. The equation from Haan et al
    (1994) is

57
Answer, continued
  • Q 2.5H2.5, where Q is in cfs and H is in feet
  • Q2.5(0.53)2.50.511 cfs or 0.51 cfs
  • Q0.51 cfs60sec/min7.48gal/cf230 gpm
  • Note Both answers contain 2 significant figures

58
Orifice Flow
  • Submerged vs Free Outlet
  • Shapes affecting C

59
Submerged Orifice
60
Free Discharge Orifice
61
Orifice Coefficients
62
Example
  • Markers Mark distillery just moved a 3 diameter
    barrel of their bourbon over their charcoal
    filter bed to drain the bourbon into the system
    to be bottled. The bung plug is removed
    instantaneously, allowing barrel strength bourbon
    to flow freely from the 2 diameter bung, which
    can be considered a sharp-edged orifice. What is
    the initial flow rate (assuming same specific
    gravity as water, which is an incorrect
    assumption)?

63
Answers
  • A 0.5 cfs
  • B 83 gpm
  • C 26.6 gpm
  • D 200 L/hr

64
Solution
  • Q0.61A(2g)0.5h0.5
  • 0.61(p12)(232.2f/s/s)0.530.5
  • 0.613.1415/144(64.4)0.530.5
  • 0.185 cfs
  • Q83 gpm (answer B)

65
Pipe flow
  • When considering pipe flow in a structure,
    Bernoullis equation is used

Frictional losses are multiples of the velocity
head (V2/2g) and are additive.
66
Head loss under pipe flow
  • Entrance loss (Ke)
  • Bend loss (Kb)
  • Pipe friction loss (Kc)
  • Each coefficient is documented in references

Considering the Bernoulli equation for a
spillway, the pressure at entrance and exit is
atmospheric, the elevation difference is the
water surface elevation difference between
upstream and downstream, and the remaining term
is the velocity head plus losses
67
Consider the following
68
Pipe flow
69
Spillway considerations
  • A given spillway may have several discharge
    relationships (weir, orifice, pipe) depending
    upon the head (stage). The stage discharge curve
    then becomes a combination curve, with the type
    of relationship allowing the highest flow at a
    given head in control.
  • Consider a drop inlet control structure

70
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71
Stage-Discharge Curve
72
Example
  • An 18 CMP with an 18 vertical riser is used as
    the principal spillway for a pond. The pipe is
    50 long with one 90 bend. The top of the inlet
    is 10 above the bottom of the outlet. Develop
    the stage-discharge relationship assuming a free
    outfall.

73
Weir flow
Basic equation
Given 18 riser, length of weir is 2pr, or 4.7,
so
74
Orifice flow
Basic orifice equation
Given 18 riser and assuming C of 0.6,
75
Pipe flow
Basic pipe flow equation
After looking up each parameter
76
Stage-Discharge Relationship
77
Questions on spillway hydraulics?
78
Open Channel Flow
  • Flow through open channels is another important
    area to consider and review. Velocity and flow
    rate are usually calculated using Mannings
    equation, which considers flow geometry, channel
    roughness and slope.

79
Mannings Equation
Where V flow velocity in fps Rh Hydraulic
Radius in ft S Energy gradeline slope in ft/ft
(bed slope for normal flow) n Manning
coefficient 1.49 conversion from SI to English
units Hydraulic radius is the flow area divided
by the wetted perimeter.
80
Open Channel Flow Channel Geometry
81
Manning n values
82
Example
  • What is the flow rate for a rectangular finished
    (clean) concrete channel with a base width of 8,
    channel slope of 0.5, with a normal water
    depth of 2?
  • A 140 cfs
  • B 8.5 cfs
  • C 100 cfs
  • D 200 cfs

83
Solution
n is 0.015, Rh is 82 sq.ft./(282) ft, S is
0.005 ft/ft, so V 8.5 ft/sec Q VA 8.5
ft/sec16 sq.ft. 140 cfs
84
Vegetated Waterway Design
  • The design of a vegetated waterway is an
    iterative process, considering both capacity when
    the grass is unmowed and hence higher resistance
    to flow and stability when recently mowed and
    more susceptible to bed scour at high flow
    velocities. Fortunately, the EFM has tables of
    suitable channel dimensions.

85
Design steps from EFH
86
Example
  • A subdivision produces a peak runoff rate of 60
    cfs from a 10yr-24hr rainfall. A vegetated
    waterway with an average slope of 3 is to be
    planted with Kentucky bluegrass. The soil at the
    waterway site is easily eroded. The waterway
    will be constructed with a parabolic shape. What
    top width and depth are required (ignoring
    freeboard)?

87
Choices
  • A 20, 2
  • B 18.5, 1.1
  • C 15, 1.5
  • D 12, 0.6

88
Permissible Velocity
Kentucky bluegrass on a 3 slope easily eroded
soil can handle up to 5 fps.
89
Resistance to flow
Kentucky bluegrass has a C resistance when
unmowed and a D resistance when cut to 2 height
90
EFM table
Reading the chart for 60cfs, V1 of 5fps, a top
width of 18.5 with a depth of 1.1 is suitable,
so answer B.
91
Questions on open channel flow or vegetated
waterways?
Questions about anything in the whole
presentation?
92
Thanks!
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