- 1 A A Wide Channel Conveys Water At 8m S 1 Per Metre M Width Of The Channel Assume The Velocity Distribution Coeffi 1 (116.34 KiB) Viewed 47 times
can you please post full solution of this question (PART A) step by step. thank you
Please use this formula book images to solve this question question
- 1 A A Wide Channel Conveys Water At 8m S 1 Per Metre M Width Of The Channel Assume The Velocity Distribution Coeffi 2 (93.79 KiB) Viewed 47 times
- 1 A A Wide Channel Conveys Water At 8m S 1 Per Metre M Width Of The Channel Assume The Velocity Distribution Coeffi 3 (82.55 KiB) Viewed 47 times
- 1 A A Wide Channel Conveys Water At 8m S 1 Per Metre M Width Of The Channel Assume The Velocity Distribution Coeffi 4 (93.55 KiB) Viewed 47 times
- 1 A A Wide Channel Conveys Water At 8m S 1 Per Metre M Width Of The Channel Assume The Velocity Distribution Coeffi 5 (77.95 KiB) Viewed 47 times
- 1 A A Wide Channel Conveys Water At 8m S 1 Per Metre M Width Of The Channel Assume The Velocity Distribution Coeffi 6 (181.38 KiB) Viewed 47 times
- 1 A A Wide Channel Conveys Water At 8m S 1 Per Metre M Width Of The Channel Assume The Velocity Distribution Coeffi 7 (86.64 KiB) Viewed 47 times
- 1 A A Wide Channel Conveys Water At 8m S 1 Per Metre M Width Of The Channel Assume The Velocity Distribution Coeffi 8 (91.99 KiB) Viewed 47 times
- 1 A A Wide Channel Conveys Water At 8m S 1 Per Metre M Width Of The Channel Assume The Velocity Distribution Coeffi 9 (95.17 KiB) Viewed 47 times
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) P B R D (Dm) by by b+ 2y B у b+ 2y (b + zyly (b + zyly (b + zyly b + 2y (1 + z2)1/2 b + 2zy b + 2y (1 + z2,112 b + 2zy zy y 2y2 2y (1 + z2)12 2zy 2 (1 + z 2112 + 2 (- sin ) de Ꮎ do (0 - sin o) de (0 - sin o) de do sin (0/2) 8 2 40 8 sin (0/2) Hydraulic diameter 4A D= Р
CONTINUITY EQUATION дQ ДА + дх at = 0 Q = V1A1 = V2A2 BERNOULLI EQUATION: H = (2+ ycos?(0) + a = (2+3 2g Coriolis and Boussinesq coefficients Channel τ α 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 n Strickler equation: n = 0.047d3/6 Chezy equation: v = CR1/251/2 = CVRS Froude Number: V Fr = gy
Reynolds number: ρνD Re = и Darcy-Weisbach: Laminar 64 Re < 2000 Re . Smooth turbulent (Blasius and Karman-Nikuradse): 0.3164 1 f= Re < 1x 105 者 = 2.0 log10(Re/7) - - 0.8 Rel4 Fully turbulent (Colebrook-White) and fully rough = 2.0 log10 + 1.14 t=( , DH ks = -2.0 log10 + 2.51 Reds 3.71D ROUGHNESS HEIGHT OF MATERIAL Material € (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 0011 - 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
FLOW AREA A WETTED HYDRAULIC PERIMETER P RADIUS R SHAPE SECTION B Trapezoidal 1 ly y(b+ y cota) 2y bt sin a y(b+ y cota) 2y CY Z b + b- sin a B Triangular ya cota 2y sin c y cos 2 y α Rectangular by b+2y by b+2y b→ 포 y Wide flat by b у b>>y> Circular (a-sina) (1 - sina) aD -D- PRESSURE IN AN OPEN CHANNEL Static pressure: Pstatic = yz = pgz Pressure for open channel: = p(z) = ydcos(0) p = yzcos(0)
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: Ib/ft2 = 0.5 x diameter in in. kg/m2 = diameter in cm (approx.) 2 10000 9000 8000 7000 6000 5000 4000 8.800 3000 2000 Critical tractive force (g/m”) 1000 $80 700 600 500 400 NK 1.000 Recommended value for canals with high content of fine sediment in the water 0.700 11111111 0.600 Fortier and Scobey: recommended 0.500 for canals in fine sand with 0.400 water containing colloids H0.300 U.S.B.R.: canals with 2.5% 0.200 colloids in water U.S.B.R.: canals with TTTTTT Schoklitsch: recommended 0.1% colloids in water for canals in sand. ENK 0.100 Recommended value for canals 8:888 Nuernberg Kulturamt (NK) with low content of fine -0.070 sediment in the water 0.060 IIIIII 10.050 NK Recommended value for canals in coarse maz noncohesive material size 25% larger 0.040 11111 0.030 Recommended values for canals with clear water DIO 0.020 Straub values of critical tractive force U.S.B.R.: canals with clear water 0.010 0.009 8:808 Fortier and Scobey: recommended 40.007 ffor canals in fine sand and clear water 0.006 40.005 Critical tractive force (1b/ft?) 300 Zaza 200 100 8 687888 30 0.004 0.003 10L 0.1 2 3 0.2 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) RABIDLY AND GRADUALLY VARIED FLOW EQUATIONS = or E = (y+ae22) +α Specific Energy: E = (y+a a) Specific Momentum: S = Ay + Head loss: E, - E2 = AE/L = S, -Sp Hydraulic Jump: [V1+8Fr, - 1] GA 2 Y2 Y1 Critical depth, velocity and Slope: For trapezoidal cross section: yc: 0 = 1 Q2T GAC3 , Vc = ga Bs Sc gn2 P R1/3 302 For rectangular cross section: yo = Sc = G Dmcn2 Vc = gy Vb2g R 3
PYSICALS PROPERTIES OF WATER Physical Properties of Water (SI Units) Vapor Dynamic viscosity Kinematic viscosity Surface tension Temperature °C Specific weight Density 7 р kN/m kg/m u* 1036 VX 1066 pressure Pv kN/m² N-s/m2 o N/m m/s 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 0.076 5 0.0749 0.0742 0.073 5 0.0728 0.0720 0.0712 0.069 6 0.0679 0.0662 0.0644 0.0626 0.060 8 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 m3s-1 i = intensity in ms-1 A = drainage area in m2 Or where = 1 Qp Clic,p) (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: N ΣC, A, 1 А Time of concentration: where te = 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 = 0.6tc tr Тр + 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 DO initial – DO BOD P BOD4 = BODu(1 – e-kxt) = Lt = BODu e-k*t = COD= CODu(1 – e-kxt) Lt = CODu e e-kxt 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.