[7939] | 1 | """Collection of culvert routines for use with Culvert_flow in culvert_class |
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| 2 | |
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| 3 | This module holds various routines to determine FLOW through CULVERTS and SIMPLE BRIDGES |
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| 4 | |
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| 5 | |
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| 6 | |
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| 7 | |
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| 8 | Usage: |
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| 9 | |
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| 10 | |
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| 11 | |
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| 12 | """ |
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| 13 | |
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| 14 | #NOTE: |
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| 15 | # Inlet control: Delta_total_energy > inlet_specific_energy |
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| 16 | # Outlet control: Delta_total_energy < inlet_specific_energy |
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| 17 | # where total energy is (w + 0.5*v^2/g) and |
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| 18 | # specific energy is (h + 0.5*v^2/g) |
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| 19 | |
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| 20 | |
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| 21 | from math import pi, sqrt, sin, cos |
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| 22 | |
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| 23 | |
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| 24 | def boyd_generalised_culvert_model(inlet_depth, |
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| 25 | outlet_depth, |
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| 26 | inlet_velocity, |
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| 27 | outlet_velocity, |
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| 28 | inlet_specific_energy, |
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| 29 | delta_total_energy, |
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| 30 | g, |
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| 31 | culvert_length=0.0, |
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| 32 | culvert_width=0.0, |
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| 33 | culvert_height=0.0, |
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| 34 | culvert_type='box', |
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| 35 | manning=0.0, |
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| 36 | sum_loss=0.0, |
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| 37 | max_velocity=10.0, |
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| 38 | log_filename=None): |
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| 39 | |
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| 40 | """Boyd's generalisation of the US department of transportation culvert methods |
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| 41 | |
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| 42 | WARNING THIS IS A SIMPLISTIC APPROACH and OUTLET VELOCITIES ARE LIMITED TO EITHER |
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| 43 | FULL PIPE OR CRITICAL DEPTH ONLY |
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| 44 | For Supercritical flow this is UNDERESTIMATING the Outlet Velocity |
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| 45 | The obtain the CORRECT velocity requires an iteration of Depth to Establish |
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| 46 | the Normal Depth of flow in the pipe. |
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| 47 | |
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| 48 | It is proposed to provide this in a seperate routine called |
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| 49 | boyd_generalised_culvert_model_complex |
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| 50 | |
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| 51 | The Boyd Method is based on methods described by the following: |
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| 52 | 1. |
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| 53 | US Dept. Transportation Federal Highway Administration (1965) |
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| 54 | Hydraulic Chart for Selection of Highway Culverts. |
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| 55 | Hydraulic Engineering Circular No. 5 US Government Printing |
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| 56 | 2. |
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| 57 | US Dept. Transportation Federal Highway Administration (1972) |
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| 58 | Capacity charts for the Hydraulic design of highway culverts. |
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| 59 | Hydraulic Engineering Circular No. 10 US Government Printing |
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| 60 | These documents provide around 60 charts for various configurations of culverts and inlets. |
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| 61 | |
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| 62 | Note these documents have been superceded by: |
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| 63 | 2005 Hydraulic Design of Highway Culverts, Hydraulic Design Series No. 5 (HDS-5), |
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| 64 | Which combines culvert design information previously contained in Hydraulic Engineering Circulars |
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| 65 | (HEC) No. 5, No. 10, and No. 13 with hydrologic, storage routing, and special culvert design information. |
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| 66 | HEC-5 provides 20 Charts |
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| 67 | HEC-10 Provides an additional 36 Charts |
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| 68 | HEC-13 Discusses the Design of improved more efficient inlets |
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| 69 | HDS-5 Provides 60 sets of Charts |
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| 70 | |
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| 71 | In 1985 Professor Michael Boyd Published "Head-Discharge Relations for Culverts", and in |
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| 72 | 1987 published "Generalised Head Discharge Equations for Culverts". |
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| 73 | These papers reviewed the previous work by the US DOT and provided a simplistic approach for 3 configurations. |
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| 74 | |
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| 75 | It may be possible to extend the same approach for additional charts in the original work, but to date this has not been done. |
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| 76 | The additional charts cover a range of culvert shapes and inlet configurations |
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| 77 | |
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| 78 | |
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| 79 | """ |
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| 80 | |
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| 81 | from anuga.utilities.system_tools import log_to_file |
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| 82 | from anuga.config import velocity_protection |
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| 83 | from anuga.utilities.numerical_tools import safe_acos as acos |
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| 84 | |
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| 85 | local_debug ='false' |
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| 86 | if inlet_depth > 0.1: #this value was 0.01: |
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| 87 | if local_debug =='true': |
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| 88 | log.critical('Specific E & Deltat Tot E = %s, %s' |
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| 89 | % (str(inlet_specific_energy), |
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| 90 | str(delta_total_energy))) |
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| 91 | log.critical('culvert type = %s' % str(culvert_type)) |
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| 92 | # Water has risen above inlet |
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| 93 | |
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| 94 | if log_filename is not None: |
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| 95 | s = 'Specific energy = %f m' % inlet_specific_energy |
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| 96 | log_to_file(log_filename, s) |
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| 97 | |
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| 98 | msg = 'Specific energy at inlet is negative' |
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| 99 | assert inlet_specific_energy >= 0.0, msg |
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| 100 | |
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| 101 | |
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| 102 | if culvert_type =='circle': |
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| 103 | # Round culvert (use height as diameter) |
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| 104 | diameter = culvert_height |
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| 105 | |
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| 106 | """ |
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| 107 | For a circular pipe the Boyd method reviews 3 conditions |
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| 108 | 1. Whether the Pipe Inlet is Unsubmerged (acting as weir flow into the inlet) |
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| 109 | 2. Whether the Pipe Inlet is Fully Submerged (acting as an Orifice) |
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| 110 | 3. Whether the energy loss in the pipe results in the Pipe being controlled by Channel Flow of the Pipe |
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| 111 | |
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| 112 | For these conditions we also would like to assess the pipe flow characteristics as it leaves the pipe |
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| 113 | """ |
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| 114 | |
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| 115 | # Calculate flows for inlet control |
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| 116 | Q_inlet_unsubmerged = 0.421*g**0.5*diameter**0.87*inlet_specific_energy**1.63 # Inlet Ctrl Inlet Unsubmerged |
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| 117 | Q_inlet_submerged = 0.530*g**0.5*diameter**1.87*inlet_specific_energy**0.63 # Inlet Ctrl Inlet Submerged |
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| 118 | # Note for to SUBMERGED TO OCCUR inlet_specific_energy should be > 1.2 x diameter.... Should Check !!! |
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| 119 | |
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| 120 | if log_filename is not None: |
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| 121 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' % (Q_inlet_unsubmerged, Q_inlet_submerged) |
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| 122 | log_to_file(log_filename, s) |
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| 123 | Q = min(Q_inlet_unsubmerged, Q_inlet_submerged) |
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| 124 | |
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| 125 | # THE LOWEST Value will Control Calcs From here |
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| 126 | # Calculate Critical Depth Based on the Adopted Flow as an Estimate |
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| 127 | dcrit1 = diameter/1.26*(Q/g**0.5*diameter**2.5)**(1/3.75) |
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| 128 | dcrit2 = diameter/0.95*(Q/g**0.5*diameter**2.5)**(1/1.95) |
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| 129 | # From Boyd Paper ESTIMATE of Dcrit has 2 criteria as |
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| 130 | if dcrit1/diameter > 0.85: |
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| 131 | outlet_culvert_depth = dcrit2 |
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| 132 | else: |
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| 133 | outlet_culvert_depth = dcrit1 |
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| 134 | #outlet_culvert_depth = min(outlet_culvert_depth, diameter) |
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| 135 | # Now determine Hydraulic Radius Parameters Area & Wetted Perimeter |
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| 136 | if outlet_culvert_depth >= diameter: |
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| 137 | outlet_culvert_depth = diameter # Once again the pipe is flowing full not partfull |
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| 138 | flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert |
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| 139 | perimeter = diameter * pi |
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| 140 | flow_width= diameter |
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| 141 | case = 'Inlet CTRL Outlet submerged Circular PIPE FULL' |
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| 142 | if local_debug == 'true': |
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| 143 | log.critical('Inlet CTRL Outlet submerged Circular ' |
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| 144 | 'PIPE FULL') |
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| 145 | else: |
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| 146 | #alpha = acos(1 - outlet_culvert_depth/diameter) # Where did this Come From ????/ |
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| 147 | alpha = acos(1-2*outlet_culvert_depth/diameter)*2 |
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| 148 | #flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) # Pipe is Running Partly Full at the INLET WHRE did this Come From ????? |
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| 149 | flow_area = diameter**2/8*(alpha - sin(alpha)) # Equation from GIECK 5th Ed. Pg. B3 |
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| 150 | flow_width= diameter*sin(alpha/2.0) |
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| 151 | perimeter = alpha*diameter/2.0 |
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| 152 | case = 'INLET CTRL Culvert is open channel flow we will for now assume critical depth' |
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| 153 | if local_debug =='true': |
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| 154 | log.critical('INLET CTRL Culvert is open channel flow ' |
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| 155 | 'we will for now assume critical depth') |
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| 156 | log.critical('Q Outlet Depth and ALPHA = %s, %s, %s' |
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| 157 | % (str(Q), str(outlet_culvert_depth), |
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| 158 | str(alpha))) |
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| 159 | if delta_total_energy < inlet_specific_energy: # OUTLET CONTROL !!!! |
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| 160 | # Calculate flows for outlet control |
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| 161 | |
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| 162 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
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| 163 | if outlet_depth > diameter: # Outlet is submerged Assume the end of the Pipe is flowing FULL |
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| 164 | outlet_culvert_depth=diameter |
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| 165 | flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert |
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| 166 | perimeter = diameter * pi |
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| 167 | flow_width= diameter |
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| 168 | case = 'Outlet submerged' |
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| 169 | if local_debug =='true': |
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| 170 | log.critical('Outlet submerged') |
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| 171 | else: # Culvert running PART FULL for PART OF ITS LENGTH Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
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| 172 | # IF outlet_depth < diameter |
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| 173 | dcrit1 = diameter/1.26*(Q/g**0.5*diameter**2.5)**(1/3.75) |
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| 174 | dcrit2 = diameter/0.95*(Q/g**0.5*diameter**2.5)**(1/1.95) |
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| 175 | if dcrit1/diameter >0.85: |
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| 176 | outlet_culvert_depth= dcrit2 |
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| 177 | else: |
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| 178 | outlet_culvert_depth = dcrit1 |
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| 179 | if outlet_culvert_depth > diameter: |
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| 180 | outlet_culvert_depth = diameter # Once again the pipe is flowing full not partfull |
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| 181 | flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert |
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| 182 | perimeter = diameter * pi |
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| 183 | flow_width= diameter |
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| 184 | case = 'Outlet unsubmerged PIPE FULL' |
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| 185 | if local_debug =='true': |
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| 186 | log.critical('Outlet unsubmerged PIPE FULL') |
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| 187 | else: |
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| 188 | alpha = acos(1-2*outlet_culvert_depth/diameter)*2 |
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| 189 | flow_area = diameter**2/8*(alpha - sin(alpha)) # Equation from GIECK 5th Ed. Pg. B3 |
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| 190 | flow_width= diameter*sin(alpha/2.0) |
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| 191 | perimeter = alpha*diameter/2.0 |
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| 192 | case = 'Outlet is open channel flow we will for now assume critical depth' |
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| 193 | if local_debug == 'true': |
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| 194 | log.critical('Q Outlet Depth and ALPHA = %s, %s, %s' |
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| 195 | % (str(Q), str(outlet_culvert_depth), |
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| 196 | str(alpha))) |
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| 197 | log.critical('Outlet is open channel flow we ' |
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| 198 | 'will for now assume critical depth') |
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| 199 | if local_debug == 'true': |
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| 200 | log.critical('FLOW AREA = %s' % str(flow_area)) |
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| 201 | log.critical('PERIMETER = %s' % str(perimeter)) |
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| 202 | log.critical('Q Interim = %s' % str(Q)) |
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| 203 | hyd_rad = flow_area/perimeter |
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| 204 | |
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| 205 | if log_filename is not None: |
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| 206 | s = 'hydraulic radius at outlet = %f' %hyd_rad |
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| 207 | log_to_file(log_filename, s) |
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| 208 | |
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| 209 | # Outlet control velocity using tail water |
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| 210 | if local_debug =='true': |
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| 211 | log.critical('GOT IT ALL CALCULATING Velocity') |
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| 212 | log.critical('HydRad = %s' % str(hyd_rad)) |
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| 213 | culvert_velocity = sqrt(delta_total_energy/((sum_loss/2/g)+(manning**2*culvert_length)/hyd_rad**1.33333)) |
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| 214 | Q_outlet_tailwater = flow_area * culvert_velocity |
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| 215 | if local_debug =='true': |
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| 216 | log.critical('VELOCITY = %s' % str(culvert_velocity)) |
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| 217 | log.critical('Outlet Ctrl Q = %s' % str(Q_outlet_tailwater)) |
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| 218 | if log_filename is not None: |
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| 219 | s = 'Q_outlet_tailwater = %.6f' %Q_outlet_tailwater |
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| 220 | log_to_file(log_filename, s) |
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| 221 | Q = min(Q, Q_outlet_tailwater) |
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| 222 | if local_debug =='true': |
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| 223 | log.critical('%s,%.3f,%.3f' |
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| 224 | % ('dcrit 1 , dcit2 =',dcrit1,dcrit2)) |
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| 225 | log.critical('%s,%.3f,%.3f,%.3f' |
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| 226 | % ('Q and Velocity and Depth=', Q, |
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| 227 | culvert_velocity, outlet_culvert_depth)) |
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| 228 | |
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| 229 | else: |
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| 230 | pass |
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| 231 | #FIXME(Ole): What about inlet control? |
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| 232 | # ==== END OF CODE BLOCK FOR "IF" CIRCULAR PIPE |
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| 233 | |
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| 234 | #else.... |
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| 235 | if culvert_type == 'box': |
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| 236 | if local_debug == 'true': |
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| 237 | log.critical('BOX CULVERT') |
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| 238 | # Box culvert (rectangle or square) ======================================================================================================================== |
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| 239 | |
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| 240 | # Calculate flows for inlet control |
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| 241 | height = culvert_height |
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| 242 | width = culvert_width |
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| 243 | flow_width=culvert_width |
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| 244 | |
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| 245 | Q_inlet_unsubmerged = 0.540*g**0.5*width*inlet_specific_energy**1.50 # Flow based on Inlet Ctrl Inlet Unsubmerged |
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| 246 | Q_inlet_submerged = 0.702*g**0.5*width*height**0.89*inlet_specific_energy**0.61 # Flow based on Inlet Ctrl Inlet Submerged |
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| 247 | |
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| 248 | if log_filename is not None: |
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| 249 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' %(Q_inlet_unsubmerged, Q_inlet_submerged) |
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| 250 | log_to_file(log_filename, s) |
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| 251 | |
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| 252 | # FIXME(Ole): Are these functions really for inlet control? |
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| 253 | if Q_inlet_unsubmerged < Q_inlet_submerged: |
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| 254 | Q = Q_inlet_unsubmerged |
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| 255 | dcrit = (Q**2/g/width**2)**0.333333 |
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| 256 | if dcrit > height: |
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| 257 | dcrit = height |
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| 258 | flow_area = width*dcrit |
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| 259 | outlet_culvert_depth = dcrit |
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| 260 | case = 'Inlet unsubmerged Box Acts as Weir' |
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| 261 | else: |
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| 262 | Q = Q_inlet_submerged |
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| 263 | flow_area = width*height |
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| 264 | outlet_culvert_depth = height |
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| 265 | case = 'Inlet submerged Box Acts as Orifice' |
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| 266 | |
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| 267 | dcrit = (Q**2/g/width**2)**0.333333 |
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| 268 | |
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| 269 | outlet_culvert_depth = dcrit |
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| 270 | if outlet_culvert_depth > height: |
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| 271 | outlet_culvert_depth = height # Once again the pipe is flowing full not partfull |
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| 272 | flow_area = width*height # Cross sectional area of flow in the culvert |
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| 273 | perimeter = 2*(width+height) |
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| 274 | case = 'Inlet CTRL Outlet unsubmerged PIPE PART FULL' |
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| 275 | else: |
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| 276 | flow_area = width * outlet_culvert_depth |
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| 277 | perimeter = width+2*outlet_culvert_depth |
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| 278 | case = 'INLET CTRL Culvert is open channel flow we will for now assume critical depth' |
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| 279 | |
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| 280 | if delta_total_energy < inlet_specific_energy: |
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| 281 | # Calculate flows for outlet control |
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| 282 | |
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| 283 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
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| 284 | if outlet_depth > height: # The Outlet is Submerged |
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| 285 | outlet_culvert_depth=height |
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| 286 | flow_area=width*height # Cross sectional area of flow in the culvert |
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| 287 | perimeter=2.0*(width+height) |
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| 288 | case = 'Outlet submerged' |
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| 289 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
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| 290 | dcrit = (Q**2/g/width**2)**0.333333 |
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| 291 | outlet_culvert_depth=dcrit # For purpose of calculation assume the outlet depth = Critical Depth |
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| 292 | if outlet_culvert_depth > height: |
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| 293 | outlet_culvert_depth=height |
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| 294 | flow_area=width*height |
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| 295 | perimeter=2.0*(width+height) |
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| 296 | case = 'Outlet is Flowing Full' |
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| 297 | else: |
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| 298 | flow_area=width*outlet_culvert_depth |
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| 299 | perimeter=(width+2.0*outlet_culvert_depth) |
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| 300 | case = 'Outlet is open channel flow' |
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| 301 | |
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| 302 | hyd_rad = flow_area/perimeter |
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| 303 | |
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| 304 | if log_filename is not None: |
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| 305 | s = 'hydraulic radius at outlet = %f' % hyd_rad |
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| 306 | log_to_file(log_filename, s) |
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| 307 | |
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| 308 | # Outlet control velocity using tail water |
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| 309 | culvert_velocity = sqrt(delta_total_energy/((sum_loss/2/g)+(manning**2*culvert_length)/hyd_rad**1.33333)) |
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| 310 | Q_outlet_tailwater = flow_area * culvert_velocity |
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| 311 | |
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| 312 | if log_filename is not None: |
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| 313 | s = 'Q_outlet_tailwater = %.6f' % Q_outlet_tailwater |
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| 314 | log_to_file(log_filename, s) |
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| 315 | Q = min(Q, Q_outlet_tailwater) |
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| 316 | else: |
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| 317 | pass |
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| 318 | #FIXME(Ole): What about inlet control? |
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| 319 | # ==== END OF CODE BLOCK FOR "IF" BOX |
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| 320 | |
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| 321 | |
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| 322 | # Common code for circle and box geometries ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
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| 323 | if log_filename is not None: |
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| 324 | log_to_file(log_filename, 'Case: "%s"' % case) |
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| 325 | |
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| 326 | if log_filename is not None: |
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| 327 | s = 'Flow Rate Control = %f' % Q |
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| 328 | log_to_file(log_filename, s) |
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| 329 | |
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| 330 | culv_froude=sqrt(Q**2*flow_width/(g*flow_area**3)) |
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| 331 | if local_debug =='true': |
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| 332 | log.critical('FLOW AREA = %s' % str(flow_area)) |
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| 333 | log.critical('PERIMETER = %s' % str(perimeter)) |
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| 334 | log.critical('Q final = %s' % str(Q)) |
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| 335 | log.critical('FROUDE = %s' % str(culv_froude)) |
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| 336 | if log_filename is not None: |
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| 337 | s = 'Froude in Culvert = %f' % culv_froude |
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| 338 | log_to_file(log_filename, s) |
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| 339 | |
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| 340 | # Determine momentum at the outlet |
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| 341 | barrel_velocity = Q/(flow_area + velocity_protection/flow_area) |
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| 342 | |
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| 343 | # END CODE BLOCK for DEPTH > Required depth for CULVERT Flow |
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| 344 | |
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| 345 | else: # inlet_depth < 0.01: |
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| 346 | Q = barrel_velocity = outlet_culvert_depth = 0.0 |
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| 347 | |
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| 348 | # Temporary flow limit |
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| 349 | if barrel_velocity > max_velocity: |
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| 350 | if log_filename is not None: |
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| 351 | s = 'Barrel velocity was reduced from = %f m/s to %f m/s' % (barrel_velocity, max_velocity) |
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| 352 | log_to_file(log_filename, s) |
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| 353 | |
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| 354 | barrel_velocity = max_velocity |
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| 355 | Q = flow_area * barrel_velocity |
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| 356 | |
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| 357 | |
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| 358 | |
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| 359 | |
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| 360 | return Q, barrel_velocity, outlet_culvert_depth |
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| 361 | |
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| 362 | |
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