1 | """Collection of culvert routines for use with Culvert_flow in culvert_class |
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2 | |
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3 | Usage: |
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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 | |
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9 | #NOTE: |
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10 | # Inlet control: Delta_total_energy > inlet_specific_energy |
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11 | # Outlet control: Delta_total_energy < inlet_specific_energy |
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12 | # where total energy is (w + 0.5*v^2/g) and |
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13 | # specific energy is (h + 0.5*v^2/g) |
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14 | |
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15 | |
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16 | from math import pi, sqrt, sin, cos |
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17 | |
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18 | |
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19 | def boyd_generalised_culvert_model(inlet_depth, |
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20 | outlet_depth, |
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21 | inlet_specific_energy, |
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22 | delta_total_energy, |
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23 | g, |
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24 | culvert_length=0.0, |
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25 | culvert_width=0.0, |
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26 | culvert_height=0.0, |
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27 | culvert_type='box', |
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28 | manning=0.0, |
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29 | sum_loss=0.0, |
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30 | log_filename=None): |
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31 | |
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32 | """Boyd's generalisation of the US department of transportation culvert |
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33 | model |
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34 | |
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35 | The quantity of flow passing through a culvert is controlled by many factors |
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36 | It could be that the culvert is controlled by the inlet only, with it |
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37 | being unsubmerged this is effectively equivalent to the weir Equation |
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38 | Else the culvert could be controlled by the inlet, with it being |
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39 | submerged, this is effectively the Orifice Equation |
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40 | Else it may be controlled by down stream conditions where depending on |
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41 | the down stream depth, the momentum in the culvert etc. flow is controlled |
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42 | """ |
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43 | |
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44 | from anuga.utilities.system_tools import log_to_file |
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45 | from anuga.config import velocity_protection |
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46 | from anuga.utilities.numerical_tools import safe_acos as acos |
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47 | |
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48 | |
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49 | if inlet_depth > 0.01: |
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50 | # Water has risen above inlet |
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51 | |
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52 | if log_filename is not None: |
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53 | s = 'Specific energy = %f m' % inlet_specific_energy |
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54 | log_to_file(log_filename, s) |
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55 | |
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56 | msg = 'Specific energy at inlet is negative' |
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57 | assert inlet_specific_energy >= 0.0, msg |
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58 | |
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59 | |
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60 | if culvert_type == 'circle': |
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61 | # Round culvert (use width as diameter) |
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62 | diameter = culvert_width |
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63 | |
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64 | # Calculate flows for inlet control |
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65 | Q_inlet_unsubmerged = 0.421*g**0.5*diameter**0.87*inlet_specific_energy**1.63 # Inlet Ctrl Inlet Unsubmerged |
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66 | Q_inlet_submerged = 0.530*g**0.5*diameter**1.87*inlet_specific_energy**0.63 # Inlet Ctrl Inlet Submerged |
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67 | |
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68 | if log_filename is not None: |
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69 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' % (Q_inlet_unsubmerged, Q_inlet_submerged) |
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70 | log_to_file(log_filename, s) |
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71 | |
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72 | |
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73 | # FIXME(Ole): Are these functions really for inlet control? |
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74 | if Q_inlet_unsubmerged < Q_inlet_submerged: |
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75 | Q = Q_inlet_unsubmerged |
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76 | alpha = acos(1 - inlet_depth/diameter) |
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77 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
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78 | outlet_culvert_depth = inlet_depth |
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79 | case = 'Inlet unsubmerged' |
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80 | else: |
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81 | Q = Q_inlet_submerged |
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82 | flow_area = (diameter/2)**2 * pi |
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83 | outlet_culvert_depth = diameter |
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84 | case = 'Inlet submerged' |
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85 | |
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86 | |
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87 | |
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88 | if delta_total_energy < inlet_specific_energy: |
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89 | # Calculate flows for outlet control |
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90 | |
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91 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
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92 | if outlet_depth > diameter: # The Outlet is Submerged |
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93 | outlet_culvert_depth=diameter |
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94 | flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert |
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95 | perimeter = diameter * pi |
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96 | case = 'Outlet submerged' |
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97 | elif outlet_depth==0.0: |
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98 | outlet_culvert_depth=inlet_depth # For purpose of calculation assume the outlet depth = the inlet depth |
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99 | alpha = acos(1 - inlet_depth/diameter) |
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100 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
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101 | perimeter = alpha*diameter |
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102 | |
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103 | case = 'Outlet depth is zero' |
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104 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
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105 | outlet_culvert_depth=outlet_depth # For purpose of calculation assume the outlet depth = the inlet depth |
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106 | alpha = acos(1 - outlet_depth/diameter) |
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107 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
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108 | perimeter = alpha*diameter |
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109 | case = 'Outlet is open channel flow' |
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110 | |
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111 | hyd_rad = flow_area/perimeter |
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112 | |
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113 | if log_filename is not None: |
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114 | s = 'hydraulic radius at outlet = %f' %hyd_rad |
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115 | log_to_file(log_filename, s) |
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116 | |
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117 | # Outlet control velocity using tail water |
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118 | culvert_velocity = sqrt(delta_total_energy/((sum_loss/2*g)+(manning**2*culvert_length)/hyd_rad**1.33333)) |
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119 | Q_outlet_tailwater = flow_area * culvert_velocity |
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120 | |
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121 | if log_filename is not None: |
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122 | s = 'Q_outlet_tailwater = %.6f' %Q_outlet_tailwater |
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123 | log_to_file(log_filename, s) |
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124 | |
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125 | Q = min(Q, Q_outlet_tailwater) |
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126 | else: |
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127 | pass |
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128 | #FIXME(Ole): What about inlet control? |
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129 | |
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130 | |
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131 | else: |
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132 | # Box culvert (rectangle or square) |
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133 | |
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134 | # Calculate flows for inlet control |
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135 | height = culvert_height |
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136 | width = culvert_width |
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137 | |
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138 | 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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139 | 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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140 | |
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141 | if log_filename is not None: |
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142 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' %(Q_inlet_unsubmerged, Q_inlet_submerged) |
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143 | log_to_file(log_filename, s) |
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144 | |
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145 | |
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146 | # FIXME(Ole): Are these functions really for inlet control? |
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147 | if Q_inlet_unsubmerged < Q_inlet_submerged: |
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148 | Q = Q_inlet_unsubmerged |
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149 | flow_area = width*inlet_depth |
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150 | outlet_culvert_depth = inlet_depth |
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151 | case = 'Inlet unsubmerged' |
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152 | else: |
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153 | Q = Q_inlet_submerged |
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154 | flow_area = width*height |
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155 | outlet_culvert_depth = height |
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156 | case = 'Inlet submerged' |
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157 | |
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158 | if delta_total_energy < inlet_specific_energy: |
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159 | # Calculate flows for outlet control |
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160 | |
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161 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
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162 | if outlet_depth > height: # The Outlet is Submerged |
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163 | outlet_culvert_depth=height |
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164 | flow_area=width*height # Cross sectional area of flow in the culvert |
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165 | perimeter=2.0*(width+height) |
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166 | case = 'Outlet submerged' |
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167 | elif outlet_depth==0.0: |
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168 | outlet_culvert_depth=inlet_depth # For purpose of calculation assume the outlet depth = the inlet depth |
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169 | flow_area=width*inlet_depth |
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170 | perimeter=(width+2.0*inlet_depth) |
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171 | case = 'Outlet depth is zero' |
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172 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
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173 | outlet_culvert_depth=outlet_depth |
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174 | flow_area=width*outlet_depth |
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175 | perimeter=(width+2.0*outlet_depth) |
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176 | case = 'Outlet is open channel flow' |
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177 | |
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178 | hyd_rad = flow_area/perimeter |
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179 | |
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180 | if log_filename is not None: |
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181 | s = 'hydraulic radius at outlet = %f' % hyd_rad |
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182 | log_to_file(log_filename, s) |
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183 | |
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184 | # Outlet control velocity using tail water |
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185 | culvert_velocity = sqrt(delta_total_energy/((sum_loss/2*g)+(manning**2*culvert_length)/hyd_rad**1.33333)) |
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186 | Q_outlet_tailwater = flow_area * culvert_velocity |
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187 | |
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188 | if log_filename is not None: |
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189 | s = 'Q_outlet_tailwater = %.6f' % Q_outlet_tailwater |
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190 | log_to_file(log_filename, s) |
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191 | Q = min(Q, Q_outlet_tailwater) |
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192 | else: |
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193 | pass |
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194 | #FIXME(Ole): What about inlet control? |
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195 | |
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196 | |
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197 | # Common code for circle and square geometries |
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198 | if log_filename is not None: |
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199 | log_to_file(log_filename, 'Case: "%s"' % case) |
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200 | |
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201 | if log_filename is not None: |
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202 | s = 'Flow Rate Control = %f' % Q |
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203 | log_to_file(log_filename, s) |
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204 | |
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205 | |
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206 | culv_froude=sqrt(Q**2*width/(g*flow_area**3)) |
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207 | |
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208 | if log_filename is not None: |
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209 | s = 'Froude in Culvert = %f' % culv_froude |
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210 | log_to_file(log_filename, s) |
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211 | |
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212 | # Determine momentum at the outlet |
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213 | barrel_velocity = Q/(flow_area + velocity_protection/flow_area) |
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214 | |
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215 | |
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216 | else: # inlet_depth < 0.01: |
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217 | Q = barrel_velocity = outlet_culvert_depth = 0.0 |
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218 | |
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219 | return Q, barrel_velocity, outlet_culvert_depth |
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220 | |
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221 | |
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