"""Collection of culvert routines for use with Culvert_flow in culvert_class This module holds various routines to determine FLOW through CULVERTS and SIMPLE BRIDGES Usage: """ #NOTE: # Inlet control: Delta_total_energy > inlet_specific_energy # Outlet control: Delta_total_energy < inlet_specific_energy # where total energy is (w + 0.5*v^2/g) and # specific energy is (h + 0.5*v^2/g) from math import pi, sqrt, sin, cos def boyd_generalised_culvert_model(inlet_depth, outlet_depth, inlet_velocity, outlet_velocity, inlet_specific_energy, delta_total_energy, g, culvert_length=0.0, culvert_width=0.0, culvert_height=0.0, culvert_type='box', manning=0.0, sum_loss=0.0, max_velocity=10.0, log_filename=None): """Boyd's generalisation of the US department of transportation culvert methods WARNING THIS IS A SIMPLISTIC APPROACH and OUTLET VELOCITIES ARE LIMITED TO EITHER FULL PIPE OR CRITICAL DEPTH ONLY For Supercritical flow this is UNDERESTIMATING the Outlet Velocity The obtain the CORRECT velocity requires an iteration of Depth to Establish the Normal Depth of flow in the pipe. It is proposed to provide this in a seperate routine called boyd_generalised_culvert_model_complex The Boyd Method is based on methods described by the following: 1. US Dept. Transportation Federal Highway Administration (1965) Hydraulic Chart for Selection of Highway Culverts. Hydraulic Engineering Circular No. 5 US Government Printing 2. US Dept. Transportation Federal Highway Administration (1972) Capacity charts for the Hydraulic design of highway culverts. Hydraulic Engineering Circular No. 10 US Government Printing These documents provide around 60 charts for various configurations of culverts and inlets. Note these documents have been superceded by: 2005 Hydraulic Design of Highway Culverts, Hydraulic Design Series No. 5 (HDS-5), Which combines culvert design information previously contained in Hydraulic Engineering Circulars (HEC) No. 5, No. 10, and No. 13 with hydrologic, storage routing, and special culvert design information. HEC-5 provides 20 Charts HEC-10 Provides an additional 36 Charts HEC-13 Discusses the Design of improved more efficient inlets HDS-5 Provides 60 sets of Charts In 1985 Professor Michael Boyd Published "Head-Discharge Relations for Culverts", and in 1987 published "Generalised Head Discharge Equations for Culverts". These papers reviewed the previous work by the US DOT and provided a simplistic approach for 3 configurations. It may be possible to extend the same approach for additional charts in the original work, but to date this has not been done. The additional charts cover a range of culvert shapes and inlet configurations """ from anuga.utilities.system_tools import log_to_file from anuga.config import velocity_protection from anuga.utilities.numerical_tools import safe_acos as acos local_debug ='false' if inlet_depth > 0.1: #this value was 0.01: if local_debug =='true': log.critical('Specific E & Deltat Tot E = %s, %s' % (str(inlet_specific_energy), str(delta_total_energy))) log.critical('culvert type = %s' % str(culvert_type)) # Water has risen above inlet if log_filename is not None: s = 'Specific energy = %f m' % inlet_specific_energy log_to_file(log_filename, s) msg = 'Specific energy at inlet is negative' assert inlet_specific_energy >= 0.0, msg if culvert_type =='circle': # Round culvert (use height as diameter) diameter = culvert_height """ For a circular pipe the Boyd method reviews 3 conditions 1. Whether the Pipe Inlet is Unsubmerged (acting as weir flow into the inlet) 2. Whether the Pipe Inlet is Fully Submerged (acting as an Orifice) 3. Whether the energy loss in the pipe results in the Pipe being controlled by Channel Flow of the Pipe For these conditions we also would like to assess the pipe flow characteristics as it leaves the pipe """ # Calculate flows for inlet control Q_inlet_unsubmerged = 0.421*g**0.5*diameter**0.87*inlet_specific_energy**1.63 # Inlet Ctrl Inlet Unsubmerged Q_inlet_submerged = 0.530*g**0.5*diameter**1.87*inlet_specific_energy**0.63 # Inlet Ctrl Inlet Submerged # Note for to SUBMERGED TO OCCUR inlet_specific_energy should be > 1.2 x diameter.... Should Check !!! if log_filename is not None: s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' % (Q_inlet_unsubmerged, Q_inlet_submerged) log_to_file(log_filename, s) Q = min(Q_inlet_unsubmerged, Q_inlet_submerged) # THE LOWEST Value will Control Calcs From here # Calculate Critical Depth Based on the Adopted Flow as an Estimate dcrit1 = diameter/1.26*(Q/g**0.5*diameter**2.5)**(1/3.75) dcrit2 = diameter/0.95*(Q/g**0.5*diameter**2.5)**(1/1.95) # From Boyd Paper ESTIMATE of Dcrit has 2 criteria as if dcrit1/diameter > 0.85: outlet_culvert_depth = dcrit2 else: outlet_culvert_depth = dcrit1 #outlet_culvert_depth = min(outlet_culvert_depth, diameter) # Now determine Hydraulic Radius Parameters Area & Wetted Perimeter if outlet_culvert_depth >= diameter: outlet_culvert_depth = diameter # Once again the pipe is flowing full not partfull flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert perimeter = diameter * pi flow_width= diameter case = 'Inlet CTRL Outlet submerged Circular PIPE FULL' if local_debug == 'true': log.critical('Inlet CTRL Outlet submerged Circular ' 'PIPE FULL') else: #alpha = acos(1 - outlet_culvert_depth/diameter) # Where did this Come From ????/ alpha = acos(1-2*outlet_culvert_depth/diameter)*2 #flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) # Pipe is Running Partly Full at the INLET WHRE did this Come From ????? flow_area = diameter**2/8*(alpha - sin(alpha)) # Equation from GIECK 5th Ed. Pg. B3 flow_width= diameter*sin(alpha/2.0) perimeter = alpha*diameter/2.0 case = 'INLET CTRL Culvert is open channel flow we will for now assume critical depth' if local_debug =='true': log.critical('INLET CTRL Culvert is open channel flow ' 'we will for now assume critical depth') log.critical('Q Outlet Depth and ALPHA = %s, %s, %s' % (str(Q), str(outlet_culvert_depth), str(alpha))) if delta_total_energy < inlet_specific_energy: # OUTLET CONTROL !!!! # Calculate flows for outlet control # Determine the depth at the outlet relative to the depth of flow in the Culvert if outlet_depth > diameter: # Outlet is submerged Assume the end of the Pipe is flowing FULL outlet_culvert_depth=diameter flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert perimeter = diameter * pi flow_width= diameter case = 'Outlet submerged' if local_debug =='true': log.critical('Outlet submerged') else: # Culvert running PART FULL for PART OF ITS LENGTH Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity # IF outlet_depth < diameter dcrit1 = diameter/1.26*(Q/g**0.5*diameter**2.5)**(1/3.75) dcrit2 = diameter/0.95*(Q/g**0.5*diameter**2.5)**(1/1.95) if dcrit1/diameter >0.85: outlet_culvert_depth= dcrit2 else: outlet_culvert_depth = dcrit1 if outlet_culvert_depth > diameter: outlet_culvert_depth = diameter # Once again the pipe is flowing full not partfull flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert perimeter = diameter * pi flow_width= diameter case = 'Outlet unsubmerged PIPE FULL' if local_debug =='true': log.critical('Outlet unsubmerged PIPE FULL') else: alpha = acos(1-2*outlet_culvert_depth/diameter)*2 flow_area = diameter**2/8*(alpha - sin(alpha)) # Equation from GIECK 5th Ed. Pg. B3 flow_width= diameter*sin(alpha/2.0) perimeter = alpha*diameter/2.0 case = 'Outlet is open channel flow we will for now assume critical depth' if local_debug == 'true': log.critical('Q Outlet Depth and ALPHA = %s, %s, %s' % (str(Q), str(outlet_culvert_depth), str(alpha))) log.critical('Outlet is open channel flow we ' 'will for now assume critical depth') if local_debug == 'true': log.critical('FLOW AREA = %s' % str(flow_area)) log.critical('PERIMETER = %s' % str(perimeter)) log.critical('Q Interim = %s' % str(Q)) hyd_rad = flow_area/perimeter if log_filename is not None: s = 'hydraulic radius at outlet = %f' %hyd_rad log_to_file(log_filename, s) # Outlet control velocity using tail water if local_debug =='true': log.critical('GOT IT ALL CALCULATING Velocity') log.critical('HydRad = %s' % str(hyd_rad)) culvert_velocity = sqrt(delta_total_energy/((sum_loss/2/g)+(manning**2*culvert_length)/hyd_rad**1.33333)) Q_outlet_tailwater = flow_area * culvert_velocity if local_debug =='true': log.critical('VELOCITY = %s' % str(culvert_velocity)) log.critical('Outlet Ctrl Q = %s' % str(Q_outlet_tailwater)) if log_filename is not None: s = 'Q_outlet_tailwater = %.6f' %Q_outlet_tailwater log_to_file(log_filename, s) Q = min(Q, Q_outlet_tailwater) if local_debug =='true': log.critical('%s,%.3f,%.3f' % ('dcrit 1 , dcit2 =',dcrit1,dcrit2)) log.critical('%s,%.3f,%.3f,%.3f' % ('Q and Velocity and Depth=', Q, culvert_velocity, outlet_culvert_depth)) else: pass #FIXME(Ole): What about inlet control? # ==== END OF CODE BLOCK FOR "IF" CIRCULAR PIPE #else.... if culvert_type == 'box': if local_debug == 'true': log.critical('BOX CULVERT') # Box culvert (rectangle or square) ======================================================================================================================== # Calculate flows for inlet control height = culvert_height width = culvert_width flow_width=culvert_width Q_inlet_unsubmerged = 0.540*g**0.5*width*inlet_specific_energy**1.50 # Flow based on Inlet Ctrl Inlet Unsubmerged Q_inlet_submerged = 0.702*g**0.5*width*height**0.89*inlet_specific_energy**0.61 # Flow based on Inlet Ctrl Inlet Submerged if log_filename is not None: s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' %(Q_inlet_unsubmerged, Q_inlet_submerged) log_to_file(log_filename, s) # FIXME(Ole): Are these functions really for inlet control? if Q_inlet_unsubmerged < Q_inlet_submerged: Q = Q_inlet_unsubmerged dcrit = (Q**2/g/width**2)**0.333333 if dcrit > height: dcrit = height flow_area = width*dcrit outlet_culvert_depth = dcrit case = 'Inlet unsubmerged Box Acts as Weir' else: Q = Q_inlet_submerged flow_area = width*height outlet_culvert_depth = height case = 'Inlet submerged Box Acts as Orifice' dcrit = (Q**2/g/width**2)**0.333333 outlet_culvert_depth = dcrit if outlet_culvert_depth > height: outlet_culvert_depth = height # Once again the pipe is flowing full not partfull flow_area = width*height # Cross sectional area of flow in the culvert perimeter = 2*(width+height) case = 'Inlet CTRL Outlet unsubmerged PIPE PART FULL' else: flow_area = width * outlet_culvert_depth perimeter = width+2*outlet_culvert_depth case = 'INLET CTRL Culvert is open channel flow we will for now assume critical depth' if delta_total_energy < inlet_specific_energy: # Calculate flows for outlet control # Determine the depth at the outlet relative to the depth of flow in the Culvert if outlet_depth > height: # The Outlet is Submerged outlet_culvert_depth=height flow_area=width*height # Cross sectional area of flow in the culvert perimeter=2.0*(width+height) case = 'Outlet submerged' else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity dcrit = (Q**2/g/width**2)**0.333333 outlet_culvert_depth=dcrit # For purpose of calculation assume the outlet depth = Critical Depth if outlet_culvert_depth > height: outlet_culvert_depth=height flow_area=width*height perimeter=2.0*(width+height) case = 'Outlet is Flowing Full' else: flow_area=width*outlet_culvert_depth perimeter=(width+2.0*outlet_culvert_depth) case = 'Outlet is open channel flow' hyd_rad = flow_area/perimeter if log_filename is not None: s = 'hydraulic radius at outlet = %f' % hyd_rad log_to_file(log_filename, s) # Outlet control velocity using tail water culvert_velocity = sqrt(delta_total_energy/((sum_loss/2/g)+(manning**2*culvert_length)/hyd_rad**1.33333)) Q_outlet_tailwater = flow_area * culvert_velocity if log_filename is not None: s = 'Q_outlet_tailwater = %.6f' % Q_outlet_tailwater log_to_file(log_filename, s) Q = min(Q, Q_outlet_tailwater) else: pass #FIXME(Ole): What about inlet control? # ==== END OF CODE BLOCK FOR "IF" BOX # Common code for circle and box geometries ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ if log_filename is not None: log_to_file(log_filename, 'Case: "%s"' % case) if log_filename is not None: s = 'Flow Rate Control = %f' % Q log_to_file(log_filename, s) culv_froude=sqrt(Q**2*flow_width/(g*flow_area**3)) if local_debug =='true': log.critical('FLOW AREA = %s' % str(flow_area)) log.critical('PERIMETER = %s' % str(perimeter)) log.critical('Q final = %s' % str(Q)) log.critical('FROUDE = %s' % str(culv_froude)) if log_filename is not None: s = 'Froude in Culvert = %f' % culv_froude log_to_file(log_filename, s) # Determine momentum at the outlet barrel_velocity = Q/(flow_area + velocity_protection/flow_area) # END CODE BLOCK for DEPTH > Required depth for CULVERT Flow else: # inlet_depth < 0.01: Q = barrel_velocity = outlet_culvert_depth = 0.0 # Temporary flow limit if barrel_velocity > max_velocity: if log_filename is not None: s = 'Barrel velocity was reduced from = %f m/s to %f m/s' % (barrel_velocity, max_velocity) log_to_file(log_filename, s) barrel_velocity = max_velocity Q = flow_area * barrel_velocity return Q, barrel_velocity, outlet_culvert_depth