Water flows down a 15-m wide rectangular spillway and has a flow depth of 0.3m. The spillway surface is finished concret

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Water Flows Down A 15 M Wide Rectangular Spillway And Has A Flow Depth Of 0 3m The Spillway Surface Is Finished Concret 1 (163.66 KiB) Viewed 40 times

Water flows down a 15-m wide rectangular spillway and has a flow depth of 0.3m. The spillway surface is finished concrete, with a Manning coefficient of 0.015. The spillway slope is 0.11. a) Calculate the flow velocity V₁ and flowrate Q on the spillway. b) The slope downstream of the spillway is very mild but the width remains the same. Verify that a hydraulic jump can occur at the transition from spillway to the mild slope. c) Calculate the conjugate depth of the hydraulic jump y₂. d) Calculate the power "killed" by the hydraulic jump in hp (1 hp = 746 Watts or N.m/s). (This diagram is not to scale) 222222 !!!!!! V₂
APPENDIX Physical properties of Water (SI Units) Specific Weight", Temperature (°C) 0 5 10 20 30 40 50 60 70 80 90 100 Density, (kg/m³) 999.9 1000.0 999.7 998.2 995.7 992.2 988.1 983.2 977.8 971.8 965.3 958.4 Temperature (°F) 32 40 50 60 70 80 90 100 120 140 160 180 200 212 Density, (slugs/ft³)b 1.940 1.940 Y (kN/m³) 1.940 1.938 1.936 1.934 1.931 9.806 9.807 9.804 9.789 9.765 9.731 1.927 1.918 1.908 1.896 1.883 1.869 1.860 9.690 9.642 9.589 9.530 9.467 9.399 "Based on data from Handbook of Chemistry and Physics, 69th Ed., CRC Press, 1988. 'Density and specific weight are related through the equation y = pg. For this table, g = 9.807 m/s². "In contact with air. Specific Weight", Y (lb/ft³) Dynamic Viscosity, 62.42 62.43 62.41 μ (N-s/m²) 62.37 62.30 62.22 62.11 62.00 61.71 61.38 61.00 60.58 60.12 59.83 1.787 E3 1.519 E-3 1.307 E 1.002 E-3 7.975 E - 4 6.529 E4 5.468 E-4 4.665 E - 4 4.042 E 4 3.547 E 4 3.147 E 4 2.818 E4 "Based on data from R. D. Blevins, Applied Fluid Dynamics Handbook, Van Nostrand Reinhold Co., Inc., New York, 1984. Physical Properties of Water (BG/EE Units)" - Dynamic Viscosity, Kinematic Viscosity, " (lbs/ft²) V (m²/s) 3.732 E-5 3.228 E-5 2.730 E-5 2.344 E-5 2.037 E-5 1.791 E-5 1.500 E-5 1.423 E-5 1.164 E-5 9.743 E-6 8.315 E-6 7.207 E-6 6.342 E-6 5.886 E-6 1.787 E - 6 1.519 E-6 1.307 E- 1.004 E-6 8.009 E7 6.580 E- 7 5.534 E - 7 4.745 E-7 4.134 E 7 3.650 E - 7 3.260 E - 7 2.940 E 7 Kinematic Viscosity, (ft³/s) 1.924 E-5 1.664 E-5 1.407 E-5 1.210 E-5 1.052 E-5 9.262 E-6 8.233 E-6 7.383 E-6 6.067 E-6 5.106 E-6 4.385 E-6 3.827 E-6 3.393 E-6 3.165 E 6 Surface Tension, 6 (N/m) 'Density and specific weight are related through the equation ypg. For this table, g 32.174 ft/s². In contact with air. 7.56 E-2 7.49 E-2 7.42 E 7.28 E 2 7.12 E 2 6.96 E 2 6.79 E-2 6.62 E 2 6.44 E 2 6.26 E 2 6.08 E 2 5.89 E 2 Surface Tension", o (lb/ft) 5.18 E-3 5.13 E-3 5.09 E 3 5.03 E-3 4.97 E-3 4.91 E 3 4.86 E - 3 4.79 E-3 4.67 E-3 4.53 E-3 4.40 E-3 4.26 E-3 4.12 E-3 4.04 E-3 Vapor Pressure, P₂ [N/m²(abs)] "Based on data from Handbook of Chemistry and Physics, 69th Ed., CRC Press, 1988. Where necessary, values obtained by interpolation. "To obtain EE units (Ibm/ft) multiply by 32.174. 6.105 E + 2 8.722 E + 2 1.228 E + 3 E3 2.338 4.243 E + 3 7.376 E3 1.233 E4 1.992 E + 4 3.116 E + 4 4.734 E 4 7.010 E + 4 1.013 E + 5 Vapor Pressure, Po [lb/in.²(abs)] 8.854 E - 2 1.217 E - 1 1.781 E 1 2.563 E 1 3.631 E 1 5.069 E-1 6.979 E 1 9.493 E 1 1.692 E +0 2.888 E + 0 4.736 E+0 7.507 E + 0 1.152 E + 1 1.469 E + 1 Speed of Sound", с (m/s) 1403 1427 1447 1481 1507 1526 1541 1552 1555 1555 1550 1543 Speed of Sound, (ft/s) 4603 4672 4748 4814 4871 4819 4960 4995 5049 5091 5101 5195 5089 5062
Equivalent Roughness for New Pipes [Adapted from Moody (Ref. 7) and Colebrook (Ref. 8)] Equivalent Roughness, & Pipe Riveted steel Concrete Wood stave Cast iron Galvanized iron Commercial steel or wrought iron Drawn tubing Plastic, glass Component a. Elbows Regular 90°, flanged Regular 90, threaded Long radius 90°, flanged Long radius 90°, threaded Long radius 45°, flanged Regular 45, threaded Loss Coefficients for Pipe Components (h₁ = K b. 180 return bends 180° return bend, flanged 180° return bend, threaded c. Tees Line flow, flanged Line flow, threaded Branch flow, flanged Branch flow, threaded d. Union, threaded 'e. Valves Globe, fully open Angle, fully open Feet 0.003-0.03 0.001-0.01 0.0006-0.003 Gate, fully open Gate, closed Gate, closed Gate, closed Swing check, forward flow Swing check, backward flow Ball valve, fully open Ball valve, closed Ball valve, closed 0.00085 0.0005 0.00015 0.000005 0.0 (smooth) 0.3 1.5 0.2 0.2 0.4 K. =) (Data from Refs. 5, 10, 27) K₂ 0.2 1.5 0.2 0.9 1.0 2.0 0.08 10 2 0.15 0.26 2.1 17 2 0.05 5.5 Millimeters 210 0.9-9.0 0.3-3.0 0.18-0.9 0.26 0.15 0.045 0.0015 0.0 (smooth) Ynt: 90° elbow 45° elbow 180° return bend Tee Tee Union
1 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.025 0.02 0.015 0.01 0.009 0.008 Laminar flow 10² Transition range I 1 1 2110%) I I 1 4 6 10 20105 Wholly turbulent flow Smooth 10° 2010 4 68 10⁰ 2010 Re- RVD Figure 1: Moody Diagram 6 10' 2010) 0.05 0.04 0.03 0.02 0.015 0.01 0.008 0.006 10.004 음 0.002 0.001 0.0008 0.0006 0.0004 0.0002 0.0001 0.00005 0.00001
Values of the Manning Coefficient, n (Ref. 6) Wetted Perimeter A. Natural channels Clean and straight Sluggish with deep pools Major rivers B. Floodplains Pasture, farmland Light brush Heavy brush Trees C. Excavated earth channels Clean Gravelly Weedy Stony, cobbles "1 0.030 0.040 0.035 0.035 0.050 0.075 0.15 0.022 0.025 0.030 0.035 Wetted Perimeter D. Artificially lined channels Glass Brass Steel, smooth Steel, painted Steel, riveted Cast iron Concrete, finished Concrete, unfinished Planed wood Clay tile Brickwork Asphalt Corrugated metal Rubble masonry 0.010 0.011 0.012 0.014 0.015 0.013 0.012 0.014 0.012 0.014 0.015 0.016 0.022 0.025