2016 PE Review: Hydrology and Hydraulics
Michael C. Hirschi, PhD, PE Professor Emeritus Agricultural and Biological Engineering University of Illinois Daniel Yoder, I-A, PE Review 2006
Acknowledgements: Daniel Yoder, I-A, PE Review 2006 Rafael (Rafa) Muoz-Carpena, I-A, PE Review Rod Huffman, past PE Review coordinator Session Topics Hydrology Hydraulics of Structures Open Channel Flow Hydrology Hydrologic Cycle Precipitation Abstractions from Rainfall
Average over Area Return Period Abstractions from Rainfall Runoff Hydrographs Determination methods Hydraulics of Structures
Weir flow Orifice flow Pipe flow Spillway flow Stage-Discharge relationship Open Channel Flow Channel geometries Mannings equation
Triangular Trapezoid Parabolic Mannings equation Manning roughness, n Grass waterway design 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 Hydrologic Cycle From Fangmeier et al. (2006)
Time scale of individual process influences/dictates whether it is significant/used for a given situation. From Fangmeier et al. (2006) Precipitation Input to the Rainfall-Runoff process Forms include:
Snow Hail Sleet Measured directly Varies temporally and areally Rainfall Data Daily Hourly 15-minute Continuous
Reported as depth, which is really volume over a given area, over a period of time Average Rainfall Simple arithmetic average Theissen Polygon Example 1 How do different calculation methods of rainfall average compare? Consider: Raingage data Gages (clockwise from upper left): 1.9, 2.1, 1.8, 1.9, 2.1, 2.2 Arithmetic average: 2.0 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. 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) Is the watershed average
rainfall using the Theissen Polygon method most nearly: 2.0 2.1 2.2 1.9 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 (65* *2.1+55* * * *2.2)/( )=2.07, which is best represented as 2.1 given most data is 2 significant digits. Any questions on Theissen Polygons? 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. US 100yr-24hr Rainfall 100yr-24hr data from TP-40 (Hershfield (1961)
as referenced by Fangmeier et al. (2006) 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). 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 10yr-24hr map from Haan, Barfield & Hayes (1994) Example Answer is C. From map, 10yr-24hr rainfall in NE Illinois is just over 4, use 4.1 to be conservative. Questions on precipitation? 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 Runoff by other names Effective rainfall Rainfall excess 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. Rainfall/Runoff process 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. Curve Number method CN Method, continued Time of Concentration, tc CN values Runoff Volume determination 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 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 Runoff Example, continued Runoff Volume determination Answer to Runoff Example
The answer is D, 53 acre-ft.From the table, the CN for Hyd group C soil with -ac lot is 80.Using the graph with a 4.1 rainfall, runoff depth is 2.1.Volume is then 300ac*2.1in = 630 ac-in, divided by 12 is 53 ac-ft. Additional example You discover that the subdivision is actually 100 acres of ac lots on C soils, 100 acres of ac lots on D soils, 50 acres of 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 Addl Runoff Example, cont. Answer The correct answer is C, 80.Use an area-weighted average, similar to Theissen method.The respective CN values for ac on C, ac on D, ac on B and townhouses on A are 80, 85, 75 & 77.The area-weighted CN is then (80*100+85*100+75*50+77*50)/300 = 80.33, which is more appropriately 80. 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: Peak Runoff Discharge 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 = 0.2*S = 0.5. Ia/P = 0.5/4.1=0.122. Tc = 2500^0.8*(1000/80-9)^0.7/1140/2^0.5 =0.8hr Peak Runoff Discharge Example solution From graph, with Ia/P of and Tc of 0.8hr, unit peak discharge is 0.57 cfs/ac/in or qp = 0.57*300*2.1 = 360 cfs 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 0.4*300*4 = 480 cfs Questions on runoff? 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. Weirs Sharp-crested Broad-crested Weir Equation (from EFH-Ch03 Hydraulics) Sharp-Crested Weir (from EFH-Ch03 Hydraulics) More complex weirs (from Haan et al., 1994) 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 cfs C gpm D.A & B Answer The answer is D.The equation from Haan et al (1994) is: Answer, continued Q = 2.5*H^2.5, where Q is in cfs and H is in feet
Q=2.5*(0.53)^2.5=0.511 cfs or 0.51 cfs Q=0.51 cfs*60sec/min*7.48gal/cf=230 gpm Note:Both answers contain 2 significant figures Orifice Flow Submerged vs Free Outlet Shapes affecting C Submerged Orifice Free Discharge Orifice Orifice Coefficients 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)? Answers A:0.5 cfs B:83 gpm C: gpm D:200 L/hr Solution Q=0.61*A*(2*g)^0.5*h^0.5
=0.61*(*1^2)*(2*32.2f/s/s)^0.5*3^0.5 =0.61*3.1415/144*(64.4)^0.5*3^0.5 =0.185 cfs Q=83 gpm (answer B) 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. 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 Consider the following Pipe flow 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: Stage-Discharge Curve 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. Weir flow Basic equation:
Given 18 riser, length of weir is 2r, or 4.7, so Orifice flow Basic orifice equation:
Given 18 riser and assuming C of 0.6, Pipe flow Basic pipe flow equation: After looking up each parameter: Stage-Discharge Relationship Questions on spillway hydraulics? 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. 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. Open Channel Flow Channel Geometry Manning n values 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 Solution n is 0.015, Rh is 8*2 sq.ft./(2+8+2) ft, S is 0.005 ft/ft, so
V = 8.5 ft/sec Q = V*A= 8.5 ft/sec*16 sq.ft. = 140 cfs 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. Design steps from EFH: 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)? Choices A:20, 2 B:18.5, 1.1 C:15, 1.5 D:12, 0.6 Permissible Velocity can handle up to 5 fps.
Kentucky bluegrass on a 3% slope easily eroded soil can handle up to 5 fps. Resistance to flow Kentucky bluegrass has a C resistance when unmowed
and a D resistance when cut to 2 height 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. Questions on open channel flow or vegetated waterways?
Questions about anything in the whole presentation? Thanks!