1 | #! /usr/bin/python |
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2 | |
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3 | # To change this template, choose Tools | Templates |
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4 | # and open the template in the editor. |
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5 | |
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6 | __author__="steve" |
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7 | __date__ ="$23/08/2010 5:18:51 PM$" |
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8 | |
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9 | |
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10 | |
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11 | def boyd_box(height, width, flow_width, inflow_specific_energy): |
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12 | """Boyd's generalisation of the US department of transportation culvert methods |
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13 | |
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14 | WARNING THIS IS A SIMPLISTIC APPROACH and OUTLET VELOCITIES ARE LIMITED TO EITHER |
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15 | FULL PIPE OR CRITICAL DEPTH ONLY |
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16 | For Supercritical flow this is UNDERESTIMATING the Outlet Velocity |
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17 | The obtain the CORRECT velocity requires an iteration of Depth to Establish |
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18 | the Normal Depth of flow in the pipe. |
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19 | |
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20 | It is proposed to provide this in a seperate routine called |
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21 | boyd_generalised_culvert_model_complex |
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22 | |
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23 | The Boyd Method is based on methods described by the following: |
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24 | 1. |
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25 | US Dept. Transportation Federal Highway Administration (1965) |
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26 | Hydraulic Chart for Selection of Highway Culverts. |
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27 | Hydraulic Engineering Circular No. 5 US Government Printing |
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28 | 2. |
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29 | US Dept. Transportation Federal Highway Administration (1972) |
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30 | Capacity charts for the Hydraulic design of highway culverts. |
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31 | Hydraulic Engineering Circular No. 10 US Government Printing |
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32 | These documents provide around 60 charts for various configurations of culverts and inlets. |
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33 | |
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34 | Note these documents have been superceded by: |
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35 | 2005 Hydraulic Design of Highway Culverts, Hydraulic Design Series No. 5 (HDS-5), |
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36 | Which combines culvert design information previously contained in Hydraulic Engineering Circulars |
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37 | (HEC) No. 5, No. 10, and No. 13 with hydrologic, storage routing, and special culvert design information. |
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38 | HEC-5 provides 20 Charts |
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39 | HEC-10 Provides an additional 36 Charts |
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40 | HEC-13 Discusses the Design of improved more efficient inlets |
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41 | HDS-5 Provides 60 sets of Charts |
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42 | |
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43 | In 1985 Professor Michael Boyd Published "Head-Discharge Relations for Culverts", and in |
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44 | 1987 published "Generalised Head Discharge Equations for Culverts". |
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45 | These papers reviewed the previous work by the US DOT and provided a simplistic approach for 3 configurations. |
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46 | |
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47 | 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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48 | The additional charts cover a range of culvert shapes and inlet configurations |
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49 | |
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50 | """ |
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51 | |
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52 | # Calculate flows for inflow control |
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53 | |
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54 | Q_inflow_unsubmerged = 0.540*g**0.5*width*inflow_specific_energy**1.50 # Flow based on inflow Ctrl inflow Unsubmerged |
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55 | Q_inflow_submerged = 0.702*g**0.5*width*height**0.89*inflow_specific_energy**0.61 # Flow based on inflow Ctrl inflow Submerged |
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56 | |
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57 | if log_filename is not None: |
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58 | s = 'Q_inflow_unsubmerged = %.6f, Q_inflow_submerged = %.6f' %(Q_inflow_unsubmerged, Q_inflow_submerged) |
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59 | log_to_file(log_filename, s) |
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60 | |
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61 | # FIXME(Ole): Are these functions really for inflow control? |
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62 | if Q_inflow_unsubmerged < Q_inflow_submerged: |
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63 | Q = Q_inflow_unsubmerged |
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64 | dcrit = (Q**2/g/width**2)**0.333333 |
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65 | if dcrit > height: |
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66 | dcrit = height |
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67 | flow_area = width*dcrit |
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68 | outflow_culvert_depth = dcrit |
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69 | case = 'inflow unsubmerged Box Acts as Weir' |
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70 | else: |
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71 | Q = Q_inflow_submerged |
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72 | flow_area = width*height |
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73 | outflow_culvert_depth = height |
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74 | case = 'inflow submerged Box Acts as Orifice' |
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75 | |
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76 | dcrit = (Q**2/g/width**2)**0.333333 |
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77 | |
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78 | outflow_culvert_depth = dcrit |
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79 | if outflow_culvert_depth > height: |
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80 | outflow_culvert_depth = height # Once again the pipe is flowing full not partfull |
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81 | flow_area = width*height # Cross sectional area of flow in the culvert |
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82 | perimeter = 2*(width+height) |
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83 | case = 'inflow CTRL outflow unsubmerged PIPE PART FULL' |
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84 | else: |
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85 | flow_area = width * outflow_culvert_depth |
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86 | perimeter = width+2*outflow_culvert_depth |
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87 | case = 'inflow CTRL Culvert is open channel flow we will for now assume critical depth' |
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88 | |
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89 | if delta_total_energy < inflow_specific_energy: |
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90 | # Calculate flows for outflow control |
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91 | |
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92 | # Determine the depth at the outflow relative to the depth of flow in the Culvert |
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93 | if outflow_depth > height: # The outflow is Submerged |
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94 | outflow_culvert_depth=height |
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95 | flow_area=width*height # Cross sectional area of flow in the culvert |
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96 | perimeter=2.0*(width+height) |
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97 | case = 'outflow submerged' |
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98 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
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99 | dcrit = (Q**2/g/width**2)**0.333333 |
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100 | outflow_culvert_depth=dcrit # For purpose of calculation assume the outflow depth = Critical Depth |
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101 | if outflow_culvert_depth > height: |
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102 | outflow_culvert_depth=height |
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103 | flow_area=width*height |
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104 | perimeter=2.0*(width+height) |
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105 | case = 'outflow is Flowing Full' |
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106 | else: |
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107 | flow_area=width*outflow_culvert_depth |
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108 | perimeter=(width+2.0*outflow_culvert_depth) |
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109 | case = 'outflow 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 outflow = %f' % hyd_rad |
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115 | log_to_file(log_filename, s) |
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116 | |
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117 | # outflow 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_outflow_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_outflow_tailwater = %.6f' % Q_outflow_tailwater |
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123 | log_to_file(log_filename, s) |
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124 | Q = min(Q, Q_outflow_tailwater) |
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125 | |
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126 | return Q |
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127 | |
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128 | |
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129 | if __name__ == "__main__": |
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130 | |
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131 | |
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132 | g=9.81 |
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133 | culvert_slope=0.1 # Downward |
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134 | |
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135 | inlet_depth=2.0 |
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136 | outlet_depth=0.0 |
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137 | |
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138 | inlet_velocity=0.0, |
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139 | outlet_velocity=0.0, |
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140 | |
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141 | culvert_length=4.0 |
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142 | culvert_width=1.2 |
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143 | culvert_height=0.75 |
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144 | |
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145 | culvert_type='box' |
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146 | manning=0.013 |
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147 | sum_loss=0.0 |
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148 | |
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149 | inlet_specific_energy=inlet_depth #+0.5*v**2/g |
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150 | z_in = 0.0 |
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151 | z_out = -culvert_length*culvert_slope/100 |
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152 | E_in = z_in+inlet_depth # + |
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153 | E_out = z_out+outlet_depth # + |
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154 | delta_total_energy = E_in-E_out |
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155 | |
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156 | Q = boyd_box(culvert_height, culvert_width, culvert_width, inlet_specific_energy) |
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157 | |
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158 | print 'Q ',Q |
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