Design Data 16. Partial Flow Conditions For Culverts. x S o Q F = C 1 = (3) A F V F Q = x A x R2/3 x S o n 1/2 (2) 1 DD 16 (07/09)

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1 Desig Data 16 Partial Flow Coditios For Culverts Sewers, both saitary ad storm, are desiged to carry a peak flow based o aticipated lad developmet. The hydraulic capacity of sewers or culverts costructed of precast circular cocrete pipe flowig full uder gravity coditios o a kow slope Is readily calculated from the Maig Formula. Most sewers, however, are desiged to operate uder partial flow coditios. Culverts operate uder either ilet cotrol or outlet cotrol. The type of cotrol uder which a particular culvert operates is depedet upo all the hydraulic factors preset. Culverts operatig uder ilet cotrol will always flow partially full while those operatig uder outlet cotrol ca flow full or partially full. Determiatio of the depth ad velocity of flow i pipe flowig partially full is therefore frequetly ecessary. This desig data presets a method for determiig the values of the partial flow depth ad velocity i circular cocrete pipe through the use of a series of partial flow curves which elimiate tedious trial ad error computatios. A complete discussio of the hydraulics of sewers is preseted i Desig Data 4, ad the hydraulics of culverts is preseted i Desig Data 8. Hydraulics of Cocrete Pipe The most widely accepted formula for evaluatig the hydraulic capacity of opressure pipe is the Maig Formula. This formula is: Where: Q x A x R2/3 x S o (1) Q flow quatity, cubic foot per secod Maig s roughess coefficiet A cross-sectioal area of flow, square feet R hydraulic radius, feet slope, feet of vertical drop per foot of horizotal distace Tables 1-3 list the full flow area, A F, hydraulic radius, R, ad a costat,. For a specific pipe size uder full flow coditios, the first three terms of the right had side of Maig s Formula equal a costat (/) x A x R 2/3 ]. Values of are preseted for the more commoly used values,.1,.11,.12, ad.13, for the roughess coefficiet for precast cocrete pipe. Utilizig the appropriate value of, ad from Tables 1-3, the full flow quatity,, may be determied from Maig s Formula coveietly expressed as: x S o (2) Oce the full flow quatity,, has bee determied, the average velocity,, for full flow coditios may be calculated from the basic hydraulic relatioship: Where: (3) A F flow quatity, flowig full, cubic feet per secod the average velocity, flowig full, feet per secod A F cross-sectioal area of flow, flowig full, square feet PARTIAL FLOW HYDRAULIC ELEMENTS For ay size of pipe, curves showig the partial flow relatioship of the hydraulic elemets, flow quatity, area of flow, hydraulic radius, ad velocity of flow i terms of the full flow coditios ca be plotted. Figures 1-4 provide such hydraulic elemet curves for circular, elliptical ad arch cocrete pipe. Desig method To determie the value of ay oe of the partial flow hydraulic elemets for circular cocrete pipe, the followig three step desig method is suggested: 1. Determie the full flow quatity,, ad velocity,, utilizig Tables 1-3 or other appropriate methods. 2. Determie the value of the ratio of partial flow to full flow of the kow hydraulic elemets. 3. Determie the values of the ukow hydraulic elemets through the use of the partial flow curves. 1

2 EXAmple 1 Example 2 Give: A 48-ich diameter circular cocrete pipe storm sewer, with equal to.12 ad flowig oe-third full. Slope required to maitai a miimum velocity of 3 feet per secod. Give: A vertical elliptical cocrete sewer is desiged to flow 3 /4 full with a desig flow, Q, of 2 cubic feet per secod. The slope is.1 ad is equal to.13. The required pipe size. Solutio: Eter Figure 1 o the vertical scale at Depth of Flow.33 ad project a horizotal lie to the curved lie represetig velocity. O the horizotal scale directly beeath the poit of itersectio read a value of 1 which represets the proportioal value for full flow: V 1 Sice the actual velocity required is 3 feet per secod: Solutio: Eter Figure 2 at a depth of flow of 5 o the vertical scale. Project a lie to the flow curve, Q, ad from the itersectio, project a vertical lie to the horizotal scale ad read a value of 7 which represets the proportioal value for full flow: Q 7 Sice the actual flow required is 2 cubic feet per secod: cubic feet per secod Eterig Table 1 at a pipe diameter of 48 iches ad a value of.12, the value is 1556 ad A F is square feet. Combiig Equatios 2 ad 3 ad solvig for : A F 2 (3.7) (12.566) feet per foot Aswer: The slope requires to maitai a miimum velocity of 3 feet per secod at o-third full is.89 feet per foot. 2 Aswer: Usig Equatio 2, to calculate : S o 23 (.1) 23 Eterig Table 2 with equal to 23, ad equal to.13, the vertical elliptical pipe with a value equal to, or greater that 23 is 76 x 48-ich. Select a 76 x 48-ich vertical elliptical pipe. 2

3 EXAmple 3 Give: A 34 x 53-ich horizotal elliptical cocrete pipe storm sewer outfall has a value assumed to be.12 ad is to be istalled o a 1 percet slope. To meet future expasio coditios, the pipe will be desiged to flow 1 /2 full. The outlet velocity. Solutio: Eterig Table 2 at a horizotal elliptical size of 34 x 53 iches ad a value of.12, the value is 1156 ad A F is 1.2 square feet. From Equatio 2: S o 1156 x (.1) 366 cubic feet per secod The full flow velocity ca be calculated from Equatio 3: EXAmple 4 Give: A 4 x 65-ich arch cocrete storm sewer outfall has a value assumed as.12 ad is to be istalled o a 1 percet slope. To meet future expasio coditios, the pipe will be desiged to flow 1 /2 full. The outlet velocity. Solutio: Eter Table 3 at a arch size of 4 x 65 iches ad a value of.12, the value is 1783 ad A F is 14.3 square feet. From Equatio 2: S o 1783 x (.1) 564 cubic feet per secod The full flow velocity ca be calculated from Equatio 3: /A F /A F 366/ feet per secod Eter Figure 3 at o the vertical scale ad project a horizotal lie to the velocity curves. From this itersectio, project a vertical lie to the horizotal scale. The ratio of partial flow V to full flow is : V V x V 36 x V 36 feet per secod Aswer: 564/ feet per secod Eter Figure 4 at o the vertical scale ad project a horizotal lie to the velocity curve, V. From this itersectio, project a vertical lie to the horizotal scale. The ratio of partial flow V to full flow is 4: V 4 V 39 x 4 V 41 feet per secod The outlet velocity is 41 feet per secod. Aswer: The outlet velocity is 36 feet per secod. 3

4 Table 1 Full Flow Coefficiet Values Circular Cocrete Pipe D Pipe Diameter A Area (Square Feet) R Hydraulic Radius (Feet) Value of x A x R2/

5 Table 2 Full Flow Coefficiet Values Elliptical Cocrete Pipe Pipe Size R x S (HE) S x R (VE) Approximate Equivalet Circular Diameter A Area (Square Feet) R Hydraulic Radius (Feet) Value of x A x R2/ x x 3 22 x x x x x x x 6 43 x x x x x x x x x x x x x x Table 3 Full Flow Coefficiet Values Arch Cocrete Pipe Pipe Size R x S Approximate Equivalet Circular Diameter A Area (Square Feet) R Hydraulic Radius (Feet) Value of x A x R2/ x x x x x 36 1/ /8 x 43 3/4 3 15/18 x 51 1/8 36 x 58 4 x x x x12 72 x /4 x /8 x /8 x x 168 3/

6 Figure 1 Relative Velocity ad Flow i Circular Pipe for Ay Desig Depth or Flow EXAMPLE 1 AREA OF FLOW, A FLOW, Q HYDRAULIC RADIUS, R Figure 2 Relative Velocity ad Flow i Vertical Elliptical Pipe for Ay Depth of Flow EXAMPLE 2 AREA OF FLOW, A FLOW, Q

7 Figure 3 Relative Velocity ad Flow i Horizotal Elliptical Pipe for Ay Depth of Flow.3.2 EXAMPLE 3 FLOW, Q AREA OF FLOW, A Figure 4 Relative Velocity ad Flow i Arch Pipe for Ay Depth of Flow.3 FLOW, Q AREA OF FLOW, A EXAMPLE Techical data herei is cosidered reliable, but o guaratee is made or liability assumed. 7