Inlet Control Coefficients

For the dimensioning of manholes according to circular nº 5 "Bureau of Public Roads", when inlet control is considered, the dam calculation requires the coefficients K, M, c, Y and Ks:

Table A.1. Constants for Inlet Control Equations
Shape and Material	Inlet Configuration	Equation	Unsubmerged	Unsubmerged	Submerged	Submerged	Ks
Shape and Material	Inlet Configuration	Form	K	M	c	Y	Ks
Circular Concrete	Square edge w/headwall	1	0.0098	2.0	0.0398	0.67	-0.5
Circular Concrete	Groove end w/headwall	1	0.0018	2.0	0.0292	0.74	-0.5
Circular Concrete	Groove end projecting	1	0.0045	2.0	0.0317	0.69	-0.5

Circular CM	Headwall	1	0.0078	2.0	0.0379	0.69	-0.5
Circular CM	Mitered to slope	1	0.0210	1.33	0.0463	0.75	0.7
Circular CM	Projecting	1	0.0340	1.50	0.0553	0.54	-0.5

Circular	Beveled ring, 45° bevels	1	0.0018	2.50	0.0300	0.74	-0.5
Circular	Beveled ring, 33.7° bevels*	1	0.0018	2.50	0.0243	0.83	-0.5

Rect. Box Concrete	30° to 75° wingwall flares	1	0.026	1.0	0.0347	0.81	-0.5
Rect. Box Concrete	90° and 15° wingwall flares	1	0.061	0.75	0.0400	0.80	-0.5
Rect. Box Concrete	0° wingwall flares	1	0.061	0.75	0.0423	0.82	-0.5
Rect. Box Concrete	45° wingwall flare d = .043D	2	0.510	0.667	0.0309	0.80	-0.5
Rect. Box Concrete	18° to 33.7° wingwall flare d = .083D	2	0.486	0.667	0.0249	0.83	-0.5
Rect. Box Concrete	90° headwall w/3/4" chamfers	2	0.515	0.667	0.0375	0.79	-0.5
Rect. Box Concrete	90° headwall w/45° bevels	2	0.495	0.667	0.0314	0.82	-0.5
Rect. Box Concrete	90° headwall w/33.7° bevels	2	0.486	0.667	0.0252	0.865	-0.5
Rect. Box Concrete	3/4" chamfers; 45° skewed headwall	2	0.545	0.667	0.04505	0.73	-0.5
Rect. Box Concrete	3/4" chamfers; 30° skewed headwall	2	0.533	0.667	0.0425	0.705	-0.5
Rect. Box Concrete	3/4" chamfers; 15° skewed headwall	2	0.522	0.667	0.0402	0.68	-0.5
Rect. Box Concrete	45° bevels; 10°-45° skewed headwall	2	0.498	0.667	0.0327	0.75	-0.5

Rect. Box 3/4" chamf. Conc.	45° non-offset wingwall flares	2	0.497	0.667	0.0339	0.803	-0.5
Rect. Box 3/4" chamf. Conc.	18.4° non-offset wingwall flares	2	0.493	0.667	0.0361	0.806	-0.5
Rect. Box 3/4" chamf. Conc.	18.4° non-offset wingwall flares 30° skewed barrel	2	0.495	0.667	0.0386	0.71	-0.5

Rect. Box Top Bev. Conc.	45° wingwall flares - offset	2	0.497	0.667	0.0302	0.835	-0.5
Rect. Box Top Bev. Conc.	33.7° wingwall flares - offset	2	0.495	0.667	0.0252	0.881	-0.5
Rect. Box Top Bev. Conc.	18.4° wingwall flares - offset	2	0.493	0.667	0.0227	0.887	-0.5

Circular	Smooth tapered inlet throat	2	0.534	0.555	0.0196	0.90	-0.5
Circular	Rough tapered inlet throat	2	0.519	0.64	0.0210	0.90	-0.5

Elliptical Face	Tapered inlet-beveled edges	2	0.536	0.622	0.0368	0.83	-0.5
Elliptical Face	Tapered inlet-square edges	2	0.5035	0.719	0.0478	0.80	-0.5
Elliptical Face	Tapered inlet-thin edge projecting	2	0.547	0.80	0.0598	0.75	-0.5

Rectangular Concrete	Tapered inlet throat	2	0.475	0.667	0.0179	0.97	-0.5
Rectangular Concrete	Side tapered-less favorable edges	2	0.56	0.667	0.0446	0.85	-0.5
Rectangular Concrete	Side tapered-more favorable edges	2	0.56	0.667	0.0378	0.87	-0.5
Rectangular Concrete	Slope tapered-less favorable edges	2	0.50	0.667	0.0446	0.65	-0.5
Rectangular Concrete	Slope tapered-more favorable edges	2	0.50	0.667	0.0378	0.71	-0.5

Table A.2. Constants for Inlet Control Equations for Discontinued Charts (see 2005 HDS 5).
Shape and Material	Inlet Configuration	Equation	Unsubmerged	Unsubmerged	Submerged	Submerged	Ks
Shape and Material	Inlet Configuration	Form	K	M	c	Y	Ks
Boxes CM	Thick wall projecting	1	0.0145	1.75	0.0419	0.64	-0.5
Boxes CM	Thin wall projecting	1	0.0340	1.5	0.0496	0.57	-0.5

Horizontal Ellipse Concrete	Square edge w/headwall	1	0.0100	2.0	0.0398	0.67	-0.5
Horizontal Ellipse Concrete	Groove end w/headwall	1	0.0018	2.5	0.0292	0.74	-0.5
Horizontal Ellipse Concrete	Groove end projecting	1	0.0045	2.0	0.0317	0.69	-0.5

Vertical Ellipse Concrete	Square edge w/headwall	1	0.0100	2.0	0.0398	0.67	-0.5
Vertical Ellipse Concrete	Groove end w/headwall	1	0.0018	2.5	0.0292	0.74	-0.5
Vertical Ellipse Concrete	Groove end projecting	1	0.0095	2.0	0.0317	0.69	-0.5

Pipe Arch 18" Corner radius CM	90° headwall	1	0.0083	2.0	0.0379	0.69	-0.5
Pipe Arch 18" Corner radius CM	Mitered to slope	1	0.0300	1.0	0.0463	0.75	0.7
Pipe Arch 18" Corner radius CM	Projecting	1	0.0340	1.5	0.0496	0.57	-0.5
Pipe Arch 18" Corner radius CM	Projecting	1	0.0300	1.5	0.0496	0.57	-0.5
Pipe Arch 18" Corner radius CM	No Bevels	1	0.0088	2.0	0.0368	0.68	-0.5
Pipe Arch 18" Corner radius CM	33.7° Bevels	1	0.0030	2.0	0.0269	0.77	-0.5

Pipe Arch 31" Corner radius CM	Projecting	1	0.0300	1.5	0.0496	0.57	-0.5
Pipe Arch 31" Corner radius CM	No Bevels	1	0.0088	2.0	0.0368	0.68	-0.5
Pipe Arch 31" Corner radius CM	33.7° Bevels	1	0.0030	2.0	0.0269	0.77	-0.5

Arch CM	90° headwall	1	0.0083	2.0	0.0379	0.69	-0.5
Arch CM	Mitered to slope	1	0.0300	1.0	0.0473	0.75	0.7
Arch CM	Thin wall projecting	1	0.0340	1.5	0.0496	0.57	-0.5

Table A.3. Constants for Inlet Control Equations for South Dakota Concrete Box (HY-8 User Manual and Table 11 of FHWA 2006).
Shape and Material	Inlet Configuration	Equation	Unsubmerged	Unsubmerged	Submerged	Submerged	Ks
Shape and Material	Inlet Configuration	Form	K	M	c	Y	Ks

South Dakota Concrete Box	Single barrel, Top bevel=45º, Wingwall Flare=30º	2	0.44	0.74	0.040	0.48	-0.5
South Dakota Concrete Box	Multiple barrel (2, 3, and 4 cells), Wingwall Flare=30º, Top bevel=45º, Corner Fillet=6"	2	0.47	0.68	0.04	0.62	-0.5
South Dakota Concrete Box	Single barrel (2:1 to 4:1 span-to-rise ratio), Wingwall Flare=30º, Top bevel=45º	2	0.48	0.65	0.041	0.57	-0.5
South Dakota Concrete Box	Multiple barrels (15° skewed headwall), Wingwall Flare=30º, Top bevel=45º	2	0.69	0.49	0.029	0.95	-0.5
South Dakota Concrete Box	Multiple barrels (30° to 45° skewed headwall), Wingwall Flare=30º, Top bevel=45º	2	0.69	0.49	0.027	1.02	-0.5
South Dakota Concrete Box	Single barrel, top edge 90°, Wingwall Flare=0º	2	0.55	0.64	0.047	0.55	-0.5
South Dakota Concrete Box	Single barrel, (0 and 6-inch corner fillets), Wingwall Flare=0º, Top bevel=45º, Corner Fillet=6"	2	0.56	0.62	0.045	0.55	-0.5
South Dakota Concrete Box	Multiple barrels (2, 3, and 4 cells), Wingwall Flare=0º, Top bevel=45º, Corner Fillet=6"	2	0.55	0.59	0.038	0.69	-0.5
South Dakota Concrete Box	Single barrels 2:1 to 4:1 span-to-rise ratio), Wingwall Flare=0º, Top bevel=45º	2	0.61	0.57	0.041	0.67	-0.5
South Dakota Concrete Box	Single barrel (0 and 6-inch fillets), Wingwall Flare=0º, Top Radius=8", Corner Fillet=6"	2	0.56	0.62	0.038	0.67	-0.5
South Dakota Concrete Box	Single barrel (12-inch corner fillets), Wingwall Flare=0º, Top Radius=8", Corner Fillet=12"	2	0.56	0.62	0.038	0.67	-0.5
South Dakota Concrete Box	Multiple barrels (2, 3, and 4 cells), Wingwall Flare=0º, Top Radius=8", Corner Fillet=12"	2	0.55	0.6	0.023	0.96	-0.5
South Dakota Concrete Box	Single barrel (2:1 to 4:1 span-to-rise ratio), Wingwall Flare=0º, Top Radius=8", Corner Fillet=12"	2	0.61	0.57	0.033	0.79	-0.5

Table A.4. Constants for Inlet Control Equations for Concrete Open-Bottom Arch (Chase 1999).
Shape and Material	Inlet Configuration	Equation	Unsubmerged	Unsubmerged	Submerged	Submerged	Ks
Shape and Material	Inlet Configuration	Form	K	M	c	Y	Ks
Concrete Open-Bottom Arch	Mitered to conform to slope, Wingwall Flare =0º, Top Edge=90º, span:rise=2:1	2	0.44	0.74	0.040	0.48	0.7
Concrete Open-Bottom Arch	Headwall with wingwalls, Wingwall Flare =45º, Top Edge=90º, span:rise=2:1	2	0.47	0.68	0.04	0.62	-0.5
Concrete Open-Bottom Arch	Headwall, Wingwall Flare =90º, Top Edge=90º, span:rise=2:1	2	0.48	0.65	0.041	0.57	-0.5

Concrete Open-Bottom Arch	Mitered to conform to slope, Wingwall Flare =0º, Top Edge=90º, span:rise=4:1	2	0.69	0.49	0.029	0.95	0.7
Concrete Open-Bottom Arch	Headwall with wingwalls,Wingwall Flare =45º, Top Edge=90º, span:rise=4:1	2	0.69	0.49	0.027	1.02	-0.5
Concrete Open-Bottom Arch	Headwall, Wingwall Flare =90º, Top Edge=90º, span:rise=4:1	2	0.56	0.62	0.045	0.55	-0.5

Table A.5. Constants for Inlet Control Equations for Embedded Circular Shapes (NCHRP 15-24).
Shape and Material	Inlet Configuration	Equation	Unsubmerged	Unsubmerged	Submerged	Submerged	Ks
Shape and Material	Inlet Configuration	Form	K	M	c	Y	Ks

Circular Shapes Embedded=0.2D	Projecting End, Ponded, Top Edge=thin	1	0.0860	0.58	0.0303	0.58	-0.5
Circular Shapes Embedded=0.2D	Projecting End, Channelized, Top Edge=thin	1	0.0737	0.45	0.0250	0.63	-0.5
Circular Shapes Embedded=0.2D	Mitered End 1.5H:1V	1	0.0431	0.58	0.0235	0.61	0.7
Circular Shapes Embedded=0.2D	Square Headwall, Top Edge=90º	1	0.0566	0.44	0.0198	0.69	-0.5
Circular Shapes Embedded=0.2D	Beveled End, Top Edge=45º	1	0.0292	0.57	0.0161	0.73	-0.5

Circular Shapes Embedded=0.4D	Projecting End, Ponded, Top Edge=thin	1	0.0840	0.76	0.0453	0.69	-0.5
Circular Shapes Embedded=0.4D	Projecting End, Channelized, Top Edge=thin	1	0.0927	0.59	0.0441	0.52	-0.5
Circular Shapes Embedded=0.4D	Mitered End 1.5H:1V	1	0.0317	0.77	0.0363	0.65	0.7
Circular Shapes Embedded=0.4D	Square Headwall, Top Edge=90º	1	0.0490	0.71	0.0332	0.67	-0.5
Circular Shapes Embedded=0.4D	Beveled End, Top Edge=45º	1	0.0358	0.62	0.0245	0.75	-0.5

Circular Shapes Embedded=0.5D	Projecting End, Ponded, Top Edge=thin	1	0.1057	0.69	0.0606	0.54	-0.5
Circular Shapes Embedded=0.5D	Projecting End, Channelized, Top Edge=thin	1	0.1055	0.59	0.0570	0.48	-0.5
Circular Shapes Embedded=0.5D	Mitered End 1.5H:1V	1	0.0351	0.59	0.0504	0.44	0.7
Circular Shapes Embedded=0.5D	Square Headwall, Top Edge=90º	1	0.0595	0.59	0.0402	0.65	-0.5
Circular Shapes Embedded=0.5D	Beveled End, Top Edge=45º	1	0.0464	0.46	0.0324	0.67	-0.5

Circular Shapes Embedded=0.2D	Projecting End, Ponded, Top Edge=thin	2	0.4293	0.64	0.0303	0.58	-0.5
Circular Shapes Embedded=0.2D	Projecting End, Channelized, Top Edge=thin	2	0.4175	0.62	0.0250	0.63	-0.5
Circular Shapes Embedded=0.2D	Mitered End 1.5H:1V	2	0.4002	0.63	0.0235	0.61	0.7
Circular Shapes Embedded=0.2D	Square Headwall, Top Edge=90º	2	0.4001	0.63	0.0198	0.69	-0.5
Circular Shapes Embedded=0.2D	Beveled End, Top Edge=45º	2	0.3869	0.63	0.0161	0.73	-0.5

Circular Shapes Embedded=0.4D	Projecting End, Ponded, Top Edge=thin	2	0.4706	0.69	0.0453	0.69	-0.5
Circular Shapes Embedded=0.4D	Projecting End, Channelized, Top Edge=thin	2	0.4789	0.66	0.0441	0.52	-0.5
Circular Shapes Embedded=0.4D	Mitered End 1.5H:1V	2	0.4185	0.68	0.0363	0.65	0.7
Circular Shapes Embedded=0.4D	Square Headwall, Top Edge=90º	2	0.4354	0.68	0.0332	0.67	-0.5
Circular Shapes Embedded=0.4D	Beveled End, Top Edge=45º	2	0.4223	0.67	0.0245	0.75	-0.5

Circular Shapes Embedded=0.5D	Projecting End, Ponded, Top Edge=thin	2	0.4955	0.71	0.0606	0.54	-0.5
Circular Shapes Embedded=0.5D	Projecting End, Channelized, Top Edge=thin	2	0.4955	0.69	0.0570	0.48	-0.5
Circular Shapes Embedded=0.5D	Mitered End 1.5H:1V	2	0.4419	0.68	0.0504	0.44	0.7
Circular Shapes Embedded=0.5D	Square Headwall, Top Edge=90º	2	0.0595	0.59	0.0402	0.65	-0.5
Circular Shapes Embedded=0.5D	Beveled End, Top Edge=45º	2	0.4364	0.69	0.0324	0.67	-0.5

Table A.6. Constants for Inlet Control Equations for Embedded Elliptical Shape (NCHRP 15-24).
Shape and Material	Inlet Configuration	Equation	Unsubmerged	Unsubmerged	Submerged	Submerged	Ks
Shape and Material	Inlet Configuration	Form	K	M	c	Y	Ks
Embedded Elliptical Shape	Projecting End, Ponded, Top Edge=thin	1	0.1231	0.51	0.0643	0.50	-0.5
Embedded Elliptical Shape	Projecting End, Channelized, Top Edge=thin	1	0.0928	0.54	0.0649	0.12	-0.5
Embedded Elliptical Shape	Mitered End 1.5H:1V	1	0.0599	0.60	0.0541	0.50	0.7
Embedded Elliptical Shape	Square Headwall, Top Edge=90º	1	0.0819	0.45	0.0431	0.61	-0.5
Embedded Elliptical Shape	Beveled End, Top Edge=90º	1	0.0551	0.52	0.0318	0.68	-0.5

Embedded Elliptical Shape	Projecting End, Ponded, Top Edge=thin	2	0.5261	0.65	0.0643	0.50	-0.5
Embedded Elliptical Shape	Projecting End, Channelized, Top Edge=thin	2	0.4937	0.67	0.0649	0.12	-0.5
Embedded Elliptical Shape	Mitered End 1.5H:1V	2	0.4820	0.67	0.0541	0.50	0.7
Embedded Elliptical Shape	Square Headwall, Top Edge=90º	2	0.4867	0.66	0.0431	0.61	-0.5
Embedded Elliptical Shape	Beveled End, Top Edge=90º	2	0.4663	0.63	0.0318	0.68	-0.5