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PART A & PART B in detail Thank you
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3) a) Using the SCS (soil conservation services, triangular unit hydrograph method develop the 60 minute UH for a watershed area of 15km2 and a time of concentration of 50 minutes. Sketch or plot the resulting synthetic unit hydrograph showing all significant features. (12 marks) b) Estimate the total runoff for the conditions above. (3 marks) c) The data presented in table 3.0 represents a precipitation hyetograph for this catchment. Assuming an average storm loss of 11mmhr generate the full hydrograph for the successive events indicated. Sketch or plot the resulting cumulative hydrograph. (15 marks) Time, t (hours) Precipitation (mm) 10 1 2 38 3 25 4 28 Table 3.0: Rainfall hyetograph

1. OPEN CHANNEL FLOW GEOMETRIC CROSS-SECTIONAL PROPERTIES Table 1-0: Geometric properties of four commonly used cross-sectional shapes. Shape Wetted | Тор Hydraulic Hydraulic mean Area (Click on figure perimeter width radius depth A to enlarge) P B R D (Dm) by by b+ 2y B у b + 2y (b + zyly (b + zy)y (b + zy) b + 2y (1 + z2)1/2 b + 2zy b + 2y (1 + z2)112 b + 2zy zy у zy2 2y (1 + z2)12 2zy 2 (1 + z2,12 2 (0 - sin e) d2 ed. (e - sin ) do (0 - sin e) do - do sin (8/2) 8 2 40 8 sin (0/2) Hydraulic diameter 4A D = P

FLOW AREA A WETTED HYDRAULIC PERIMETER P RADIUS R SHAPE SECTION B. Trapezoidal 1 у y(b+ y cota) 2y b + sina CY y(b+ y cota) 2y b + Z sina Triangular y2 cota 2y sin a - y cosa 2 Rectangular y b+2y by b+2y у Wide flat by b у b>>y> Circular (a-sin sin a) (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 an ДА + = 0 дх at Q = V1A1 = VzA2 BERNOULLI EQUATION: H = (x + ycos? (0) + a = ) 29 Coriolis and Boussinesq coefficients Channel α Column 1 Column2 B Column 3 Column4 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: Q = - AR2/391/2 2 =EAA n Strickler equation: n = 0.047d3/6 Chezy equation: v = CR1/251/2 = CVRS Froude Number: V Fr= Vgy

Reynolds number: ρνD Re = u Darcy-Weisbach: Laminar 64 f= Re Re < 2000 Smooth turbulent (Blasius and Karman-Nikuradse): 0.3164 Re < 1 x 103 5 = J 2.0 log10 f= - 0.8 Reff) Re! 4 Fully turbulent (Colebrook-White) and fully rough 1 2.51 = 2.0 log10 = -2.0 log10 + 1.14 DH ks ks 3.71DH + Refr ROUGHNESS HEIGHT OF MATERIAL Material E (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 Material Lined Channels: Asphalt Brick Concrete Rubble or riprap 0.013 -0.017 0.012 -0.018 0.011 -0.020 0.020 - 0.035 0.030-0.40 Vegetal Excavated or dredged channels: Earth, Straight and uniform Earth, winding, fairly uniform Rock Unmaintained 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 το = ydsin(a) or To = y d S (S is the longitudinal slope) 20 000 Line representing relations of tractive forces: 1b/ft2 = 0.5 x diameter in in. kg/m2 = diameter in cm (approx.) 10000 9000 8000 7000 6000 5000 4000 3000 2000 Critical tractive force (g/m2) 1000 900 ఆకు 700 600 500 400 NK Recommended value for canals with high content of fine sediment in the water IIIII 0.600 Fortier and Scobey: recommended 10.500 for canals in fine sand with 0.400 water containing colloids NK H0.300 U.S.B.R.: canals with 2.5% colloids in water 0.200 U.S.B.R.: canals with Schoklitsch: recommended 0.1% colloids in water for canals in sand -NK Recommended value for canals Nuemberg Kulturamt (NK) with low content of fine 10.070 sediment in the water 0.060 III 0.050 NK Recommended value for canals in coarse noncohesive material size 25% larger 0.040 1 IT H0.030 Recommended values for canals with clear water 0.020 Straub values of critical tractive force U.S.B.R.: canals with clear water 0.010 8:888 Fortier and Scobey: recommended 0.007 for canals in fine sand and clear watert 0.006 0.005 0.004 Critical tractive force (Ib/ft?) 300 200 100 888888 40 30 20 0.003 10 0.1 0.2 2 0.3 0.4 0.6 0.8 1.0 0.5 0.7 0.9 3 4 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 A22g Specific Momentum: S = Ay + gA Head loss: E1-E2 = AE/L = S, -Sg = = 2 Hydraulic Jump: Y2 = Yı = [/1 +8Fr;? - 1] ,? 1 Critical depth, velocity and Slope: For trapezoidal cross section: yc: 0 = 1 - Q2T gA B' gn2 P Sc= Vc = 943 Bs R1/3 3 For rectangular cross section: y = 02 bag Sc g Dmcna ,Vc = R3 gy

Kinematic viscosity Vapor Surface tension σ Nm ux 10 V x 1066 pressure P kN/m2 mºls 0.61 0.87 PYSICALS PROPERTIES OF WATER Physical Properties of Water (SI Units) Dynamic Specific weight Density viscosity Temperature 7 р °C kNm kg/m N-s/m² 0 9.805 999.8 1.781 5 9.807 1 000.0 1.518 10 9.804 999.7 1.307 15 9.798 999.1 1.139 20 9.789 998.2 1.002 25 9.777 997.0 0.890 30 9.764 995.7 0.798 40 9.730 992.2 0.653 9.689 988.0 0.547 9.642 983.2 0.466 70 9.589 0.404 80 9.530 971.8 0.354 90 9.466 965.3 0.315 100 9.399 958.4 0.282 1.785 1.519 1.306 1.139 1.003 0.893 0.800 0.658 0.553 0.474 0.0765 0.0749 0.0742 0.073 5 0.0728 0.0720 0.0712 0.0696 0.0679 0.0662 0.0644 0.0626 0.0608 0.0589 1.23 1.70 2.34 3.17 4.24 7.38 12.33 19.92 31.16 47.34 70.10 101.33 977.8 0.413 0.364 0.326 0.294

2. HYDROLOGY RATIONAL FORMULA: Q = CiA C = coefficient of runoff that represents the characteristics of the catchment Q = peak discharge in m3s-1 i = intensity in ms? A = drainage area in m2 Or IC(ic.p)A where 0,- (7.2) 3.6 Qp = peak discharge (m²/s) C = coefficient of runoff (irc.p) = the mean intensity of precipitation (mm/h) for a duration equal to te and an exceedence probability P A = drainage area in km? = Runoff coeffiecient: N CA ΣC, A, 1 C A Time of concentration: where t = 0.01947 20.77 5-0.385 (7.4) to = 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 = 0.6t. tr Тр = + tp 2 2.08 A ер Тр To = 2.67Tp =

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 0.70-1.95 0.50 0.40 0.20 0.10 0.70 0.60 0.40 0.30 3. WATER QUALITY 7 DO initial – DOG BOD= P BOD+ = BODu(1 - e-kxt) Lt = BODu e-ket COD = CODU(1 - e-kxt) Lt = CODu e-kut = Temperature correction (for river/stream water at a temperature of T°C) KT = K20 (T-20) 0 = temperature coefficient, it has a value of 1.056 at temperature = 20°C, and1.047 for temperatures higher than 20 °C.

Simple mass balance: Vi X BOD + V2 X BOD2 BOD mix = V1 + V2 ' CODmix Vi X COD. + V2 X COD2 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 D= Dee U + LKL ka - ki -k, -kx U U е -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 Duplup + D.Q D. = Qup + Qe C down Cup Qup + CQC Cup + Qe The travel time (tc) to the critical deficit is given by 1 k t. = In A(, White 1-D. 8 k-k k k L The critical distance is given by x = Ut

Equations for the reaeration coefficient at 20°C. If river depth > 0.6m and stream velocity < 0.55m/s, use O'Connor-Dobbins correlation JU k, = 3.9 H15 If river depth > 0.6m and stream velocity > 0.55m/s, Use Churchill-Elmore-Buckingham correlation k = 5.03 Մ0.969 H1.673 If river depth < 0.6m, use Owens-Edwards-Gibb correlation kg = 5.34 Մ0.67 H1.85 For the three equations:- U is the average river velocity (m per second) His the average river depth (m) I (°C) 0 20 50 100 Basic Properties of Water Water p (kg m*) u (Pa s) v (mºs) 1000 1.788x10-3 1.788x10-6 998 1.003x10-3 1.005x10-6 988 0.548x10-3 0.555x10 958 0.283x10- 0.295x10-6

Dissolved Oxygen Saturation Concentrations, mg/l Temperature Chloride concentration, mgL °C 0 5 000 10 000 15 000 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 12.545 12218 11.906 11.607 11320 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