2) A city discharges 126000 m3/d of primary effluent into a stream. Take the minimum flow rate of the stream to be 136 m

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2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 1 (168.42 KiB) Viewed 45 times

please post solution of QUESTION 2
* PART B & PART C*
Please use this formula book imsges to solve it. thank you.

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 2 (101.59 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 3 (87.83 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 4 (96.99 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 5 (183.85 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 6 (73.73 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 7 (68.65 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 8 (87.51 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 9 (85.09 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 10 (97.07 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 11 (80.76 KiB) Viewed 45 times

2 A City Discharges 126000 M3 D Of Primary Effluent Into A Stream Take The Minimum Flow Rate Of The Stream To Be 136 M 12 (82.19 KiB) Viewed 45 times

2) A city discharges 126000 m3/d of primary effluent into a stream. Take the minimum flow rate of the stream to be 136 m3/min. The velocity of the stream is 0.5 km/h. The BOD5 of the wastewater is 50 mg/l, with a dissolved oxygen (D.O.) concentration of Omg/l. Upstream of the mixing point, the stream has a D.O. level of 10 g/m3 and a BODultimate of 4 g/m3. Downstream of the mixing point, the stream temperature is approximately 4°C. The deoxygenation rate constant is 0.3d-1 (base e) at 20°C with a temperature coefficient of 1.13. There is significant ice cover on the stream so that reaeration is negligible. Assume there are no other inputs of waste or D.O. downstream. a) At what distance downstream of the mixing point will the minimum D.O. concentration occur and what will the D.O concentration be at that location? (20 marks) b) What will the D.O. concentration be at a point 5km downstream of the point of discharge? (5 marks) c) State clearly what your recommendations would be for someone considering acquiring a fishing business located at the 5km point. Provide the reasoning for your advice. (5 marks)

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 ly b + 2y (b + zy)y + (b + zyly (b + zyly + b + 2y (1 + z 2)1/2 b + 2zy b + 2y (1 + z2) 1/2 b + 2zy zy ly zy? 2y (1 + z2)12 2zy 2 (1 + z2)12 2 (e - sin 0) do? O do (0 - sin ) do (0 - sin 6) do d do sin (0/2) 8 2 40 8 sin (012) Hydraulic diameter 4A D= P

CONTINUITY EQUATION дQ дА + = 0 дх at Q = V1A1 = V2A2 BERNOULLI EQUATION: 321 H = (2+ ycos(0) + a 2g h = (2+ ye am Coriolis and Boussinesq coefficients Channel a Column 1 Column2 B Column3 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: 1 Q = - AR2/351/2 2 Strickler equation: n = 0.047d366 = Chezy equation: v = CR1/291/2 = CVRS Froude Number: V Fr = gy

Reynolds number: ρD Re = u Darcy-Weisbach: Laminar . f= 64 Re Re < 2000 . - 0.8 Smooth turbulent (Blasius and Karman-Nikuradse): 0.3164 1 fa Re < 1 X 10 ta = 2.0 log10(ReNT) - Fully turbulent (Colebrook-White) and fully rough Rel4 . 2.51 = 2.0 logio + 1.14 1--20w-(3-foon met = -2.0 log10 DH ks ks 3.71DH + Reff 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 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 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 To = ydsin(a) or To = y d S (S is the longitudinal slope) 4 20000 3 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 0.400 1000 Critical tractive force (g/m2) 700 600 500 400 NK 1.000 Recommended value for canals with high content 8:888 of fine sediment in the water 0.700 IIIIIIII 0.600 Fortier and Scobey: recommended 0.500 for canals in fine sand with water containing colloids NK 0.300 IIIIII U.S.B.R.: canals with 2.5% 0.200 colloids water U.S.B.R.: canals with TT Schoklitsch: recommended 0.1% colloids in water for canals in sand NK 0.100 Recommended value for canals 8:888 Nuemberg Kulturamt (NK) with low content of fine 0.070 Izza sediment in the water 0.060 IIIIII 0.050 NK Recommended value for canals in coarse 0.040 noncohesive material size 25% larger 0.030 E 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 0.009 0.008 Fortier and Scobey: recommended 0.007 for canals in fine sand and clear water 0.006 0.005 0.004 Critical tractive force (Ib/ft?) 300 200 100 88 70 60 50 40 30 20 0.003 10 0.1 0.2 3 0.3 0.4 0.6 0.8 1.0 0.5 0.7 0.9 4 5 6 7 8 9 10 20 30 40 50 60 80 100 70 90 Mean diameter (mm) 02 α 2g or A22g RABIDLY AND GRADUALLY VARIED FLOW EQUATIONS Specific Energy: E = (y+ams) E = (y+a; E Specific Momentum: Q2 S = Ay+ ga Head loss: E1 - E2 = AE/L = S, -S Hydraulic Jump: y2 = [/1+8Fr, - 1] Critical depth, velocity and Slope: For trapezoidal cross section: yc: gn2 P Vc = S = BS Bs R1/3 For rectangular cross section: 02 y = Sc = g Dmcn2 bag Vc = Vgyc R3 = 0 = 1 - 0216 9A3 LEN 3 .

FLOW AREA A WETTED HYDRAULIC PERIMETER P RADIUS R SHAPE SECTION B- Trapezoidal 1 「人。 |y 2y b + sin a α y(b+ y cota) y(b+ y cota) 2y b + sina z -- Triangular ² cota 2y sin a y cosa 2 у. α Rectangular y by b+2y by b+2y 몹 Wide flat by b у t-b>>y-1 Circular (a-sina) aD (1 - sina) PRESSURE IN AN OPEN CHANNEL Static pressure: Pstatic = yz = pgz Pressure for open channel: p(z) = ydcos(0) p=yzcos-(0)

PYSICALS PROPERTIES OF WATER Physical Properties of Water (SI Units) Dynamic viscosity Kinematic viscosity Surface tension Vapor Temperature °C UX 1036 V x 1066 o pressure P kNm? m/s 5 0 5 10 15 20 25 30 40 50 60 70 80 90 100 Specific weight Density P kN/m kg/m 9.805 999.8 9.807 1 000.0 9.804 999.7 9.798 999.1 9.789 998.2 9.777 997.0 9.764 995.7 9.730 992.2 9.689 988.0 9.642 983.2 9.589 977.8 9.530 971.8 9.466 965.3 9.399 958.4 N-s/m² 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 Nm 0.0765 0.0749 0.0742 0.0735 0.072 8 0.0720 0.0712 0.0696 0.0679 0.0662 0.0644 0.0626 0.0608 0.0589 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 ms-1 i = intensity in ms? A = drainage area in m2 Or 6 where 0,- COPA (7.2) 3.6 Qp = peak discharge (m²/s) C = coefficient of runoff (iic.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: ŽC 4 1 Ce= А Time of concentration: where t = 0.01947 0.77 5-0.385 (7.4) tc = 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 Tp = + tp 2 2.08A Qp Тр To = 2.67T =

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: 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, mg °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 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 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 9.276 9.092