- 3 A Using The Scs Soil Conservation Services Triangular Unit Hydrograph Method Develop The 60 Minute Uh For A Waters 1 (85.72 KiB) Viewed 36 times
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1. OPEN CHANNEL FLOW GEOMETRIC CROSS-SECTIONAL PROPERTIES Table 1-0: Geometric properties of four commonly used cross-sectional shapes. Shape Wetted Top Hydraulic Hydraulic mean Area (Click on figure perimeter width radius depth A to enlarge) Р B R D (Dm) by by b + 2y B у b + 2y (b + zy)y (b + zyly (b + zy)y b + 2y (1 + z2)1/2 b + 2zy b + 2y (1 + z2) 112 b + 2zy zy Гу zy2 2y (1 + z2)112 2zy 2 (1 + z2,112 2 (0 - sin e) d.2 Odo (- sin ) do ( - sin e) do d do sin (0/2) 8 2 40 8 sin (0/2) Hydraulic diameter 4A D =
FLOW AREA A WETTED HYDRAULIC PERIMETER P RADIUS R SHAPE SECTION B 몰 Trapezoidal y y(b+ y cota) 2y b + sina Q y(b+ y cota) 2y bt z -b- sin a Triangular y² cota 2y sina y cosa 2 QY by Rectangular by b+2y b+2y Wide flat by b у t-b>>y-1 aD 2 (a-sin a) ?? Circular 1-sina) PRESSURE IN AN OPEN CHANNEL Static pressure: Pstatic = yz = pgz Pressure for open channel: = p(z) = ydcos(0) p = yzcos?(0) =
CONTINUITY EQUATION дQ ДА + = 0 дх at Q = V,A1 = V₂A₂ BERNOULLI EQUATION: 02 H = (z + ycos?(0) + a + = (z+yce 29 Coriolis and Boussinesq coefficients Channel Column 1 Column2 В Column3 Column 4 - Minimum Maximum Average Minimum Maximum Average Regular channels, flumes, spillwa 1.1 1.2 1.15 1.03 1.07 1.05 Natural streams and torrents 1.15 1.5 1.3 1.05 1.17 1.1 River under ice cover 1.2 2 1.5 1.07 1.33 1.17 River valley, over flooded 1.5 2 1.75 1.17 1.33 1.25 UNIFORM FLOW EQUATIONS Manning equation: 1 Q = - AR2/351/2 n = A. Strickler equation: n = 0.047d366 Chezy equation: v = CR1/251/2 = CVRS Froude Number: V Fr = gy
Reynolds number: pud Re = u Darcy-Weisbach: Laminar 64 Re < 2000 Re . Smooth turbulent (Blasius and Karman-Nikuradse): 0.3164 1 f= Re < 1 X 105 5 -2.0 1080(Rex 7) – 08 = - Rel/4 . Fully turbulent (Colebrook-White) and fully rough 2.51 = 2.0 logio +--( J ks 3.71DH + 1.14 () DH ks = -2.0 log10 + Ref ROUGHNESS HEIGHT OF MATERIAL Material ɛ (mm) Concrete, coarse 0.25 Concrete, new smooth 0.025 Drawn tubing 0.0025 Glass.Plastic.Perspex 0.0025 Iron, cast 0.15 Sewers.old 3.0 Steel, mortar lined 0.1 Steel, rusted 0.5 Steel, structural or forged 0.025 Water mains, old 1.0 MANNING COEFFICIENT OF MATERIAL n 0.013 -0.017 0.012 -0.018 0.011 -0.020 0.020 -0.035 0.030-0.40 Material Lined Channels: Asphalt Brick Concrete Rubble or riprap Vegetal Excavated or dredged channels: Earth, Straight and uniform Earth, winding, fairly uniform Rock Urmaintained Natural Channels: (width < 31 m) Fairly regular section Irregular section with pools 0.020 -0.030 0.025 -0.040 0.030 - 0.045 0.050-0.14 0.03 -0.07 0.04 -0.10
SHEAR STRESS IN OPEN CHANEL To = ydsin(a) or To = y d S (S is the longitudinal slope) 4 20000 10000 9000 8000 Line representing relations of tractive forces: Ib/ft2 = 0.5 x diameter in in. kg/m2 = diameter in cm (approx.) 7000 6000 5000 4000 3000 2000 Critical tractive force (g/m) 1000 900 700 600 500 400 NK 1.000 Recommended value for canals with high content 0.9 of fine sediment in the water 0.700 0.600 Fortier and Scobey: recommended 0.500 for canals in fine sand with 0.400 water containing colloids NK 0.300 IIIIII U.S.B.R.: canals with 2.5% 0.200 colloids in water U.S.B.R.: canals with TTTT Schoklitsch: recommended 0.1% colloids in water for canals in sand NK 0. Recommended value for canals 8:88 Nuernberg Kulturamt (NK) with low content of fine 0.070 sediment in the water 0.060 ITITI 0.050 NK Recommended value for canals in coarse ZZZZ 0.040 noncohesive material size 25% larger 1111 11 0.030 Recommended values for canals with clear water DITT 0.020 Straub values of critical tractive force U.S.B.R.: canals with clear water 0.010 Critical tractive force (Ib/ft?) 300 200 100 90 80 60 SO 40 888 Fortier and Scobey: recommended for canals in fine sand and clear water 0.007 30 0.006 0.005 0.004 20 0.003 101 0.1 0.2 2 3 4 0.3 0.4 0.6 0.8 1.0 0.5 0.7 0.9 5 6 7 8 9 10 20 30 40 50 60 80 100 70 90 Mean diameter (mm) RABIDLY AND GRADUALLY VARIED FLOW EQUATIONS Specific Energy: E = (y+a) or E = (y + a + = A229 Specific Momentum: S = Ay+ GA Head loss: E1 - Ez = AE/L = S, -Sf Hydraulic Jump: Y2 = [/1+8Fr;? - 1] Critical depth, velocity and Slope: Q2TC For trapezoidal cross section: yc: 0 = 1 Y1 gA gn2 P Vc = Sc GA3 Bs Bs R1/3 For rectangular cross section: Yc = Q2 b2g Sc g Dmcna , Vc = RS дус
PYSICALS PROPERTIES OF WATER Physical Properties of Water (SI Units) Vapor Dynamic viscosity Kinematic viscosity Temperature °C Specific weight Density 7 р kN/m Surface tension o N/m ux 1036 V x 1066 pressure Pv kN/m² kg/m N-s/m² m/s 5 0 5 10 15 20 25 30 40 50 60 70 80 90 100 9.805 9.807 9.804 9.798 9.789 9.777 9.764 9.730 9.689 9.642 9.589 9.530 9.466 9.399 999.8 1 000.0 999.7 999.1 998.2 997.0 995.7 992.2 988.0 983.2 977.8 971.8 965.3 958.4 1.781 1.518 1.307 1.139 1.002 0.890 0.798 0.653 0.547 0.466 0.404 0.354 0.315 0.282 1.785 1.519 1.306 1.139 1.003 0.893 0.800 0.658 0.553 0.474 0.413 0.364 0.326 0.294 0.0765 0.0749 0.0742 0.0735 0.0728 0.0720 0.0712 0.0696 0.0679 0.066 2 0.0644 0.0626 0.0608 0.058 9 0.61 0.87 1.23 1.70 2.34 3.17 4.24 7.38 12.33 19.92 31.16 47.34 70.10 101.33
2. HYDROLOGY RATIONAL FORMULA: Q = CiA C = coefficient of runoff that represents the characteristics of the catchment Q = peak discharge in mºs-7 i = intensity in ms-7 A = drainage area in m2 Or 6 where Qp = Clive.p)A (7.2) 3.6 Qp = peak discharge (m²/s) C = coefficient of runoff (ic.p) = the mean intensity of precipitation (mm/h) for a duration equal to t, and an exceedence probability P A = drainage area in km² Runoff coeffiecient: ΣC, A Ce = A Time of concentration: where 1. = 0.01947 (0.77 -0.385 (7.4) t = time of concentration (minutes) L = maximum length of travel of water (m), and S= slope of the catchment = A H/L in which AH = difference in elevation between the most remote point on the catch- ment and the outlet SCS triangular unit hydrograph: tp = 0.6tc tr Тр + tp 2 2.08A Qp Тр To = 2.67T| - 4/1 + =
Runoff coeffiecient Value of C 0.05-0.10 0.15-0.20 0.18-0.22 0.30-0.50 0.60-0.75 Types of area A. Urban area (P = 0.05 to 0.10) Lawns: Sandy-soil, flat, 2% Sandy soil, steep, 7% Heavy soil, average, 2.7% Residential areas: Single family areas Multi units, attached Industrial: Light Heavy Streets B. Agricultural Area Flat: Tight clay;cultivated woodland Sandy loam;cultivated woodland Hilly: Tight clay;cultivated woodland Sandy loam;cultivated woodland 0.50-0.80 0.60-0.90 0.70–0.95 0.50 0.40 0.20 0.10 0.70 0.60 0.40 0.30 3. WATER QUALITY 7 - DO initial – DO BOD = Р BOD; = BODu(1 - e-kxt) Lt = BODu e-ket CODE = CODu(1 - e-kxt) Lt = CODų e-k+t Temperature correction (for river/stream water at a temperature of T°C) Ky = K20 (T-20) 0 = temperature coefficient, it has a value of 1.056 at temperature s 20°C, and1.047 for temperatures higher than 20 °C.
Simple mass balance: V1 X BOD + V2 X BOD2 BODmix = V1 + V2 Vi X CODA + V2 X COD2 CODmix = V1 + V2 Variation of saturation concentration of oxygen in water (mg/l) with temperature T (measured in degrees C) is given by: C = 14.65 -0.41022 T +0.00791 T² -0.00007774 T Streeter-Phelps Equation kex U. LKL D= Dee + k -kx -kx U. U. e -e Where • D-dissolved oxygen deficit (mg per litre) at a distance x (m) from the point of contamination • Do - dissolved oxygen deficit at x = 0 (mg/l) • ka is the re-aeration coefficient (per day) • U, is the river velocity (m per day) • Lo is the ultimate CBOD at x = 0 (mg/l) • kl is the BOD decay rate constant (per day) Calculation of initial oxygen deficit, or concentration of pollutant, from a point source D. DopQup + D.QE Qup+Q down Cup Qup + CQ Qup + QE The travel time (tc) to the critical deficit is given by 1 k t = to two (0-2white Ina (k, - k) 1-D. kL. 8 k-k k The critical distance is given by xe = U..
Equations for the reaeration coefficient at 20°C. If river depth > 0.6m and stream velocity < 0.55m/s, use O'Connor-Dobbins correlation VU k, = 3.9 H15 If river depth > 0.6m and stream velocity > 0.55m/s, Use Churchill-Elmore-Buckingham correlation ka 0.969 = 5.03 H1.673 If river depth < 0.6m, use Owens-Edwards-Gibb correlation U 0.67 k, = 5.34 H1.85 For the three equations:- U is the average river velocity (m per second) H is the average river depth (m) T(°C) 0 20 Basic Properties of Water Water p (kg mº) u (Pa s) v (mºs) 1000 1.788x10-3 1.788x10-6 998 1.003x10-3 1.005x10-6 988 0.548x10-3 0.555x100 958 0.283x10 0.295x10-6 50 100
Dissolved Oxygen Saturation Concentrations, mg/l Temperature Chloride concentration, mgL °C 0 5 000 10 000 15000 20 000 25 000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 14.621 14.216 13.829 13.460 13.107 12.770 12.447 12.139 11.843 11.559 11.288 11.027 10.777 10.537 10.306 10.084 9.870 9.665 9.467 9.276 9.092 13.728 13.356 13.000 12.660 12.335 12.024 11.727 11.442 11.169 10.907 10.656 10.415 10.183 9.961 9.747 9.541 9.344 9.153 8.969 8.792 8.621 12.888 12545 12.218 11.906 11.607 11.320 11.046 10.783 10.531 10.290 10.058 9.835 9.621 9.416 9.218 9.027 8.844 8.667 8.497 8.333 8.174 12.097 11.783 11.483 11.195 10.920 10.656 10.404 10.162 9.930 9.707 9.493 9.287 9.089 8.899 8.716 8.540 8.370 8.207 8.049 7.896 7.749 11.355 11.066 10.790 10.526 10.273 10.031 9.799 9.576 9.362 9.156 8.959 8.769 8.586 8.411 8.242 8.079 7.922 7.770 7.624 7.483 7.346 10.657 10.392 10.319 9.897 9.664 9.441 9.228 9.023 8.826 8.636 8.454 8.279 8.111 7.949 7.792 7.642 7.496 7.356 7.221 7.090 6.964