Lecture 8 : Hydraulic Design of Sewers and Storm Water Drains (Contd.)

Transcription

1 1 P age Module 7 : Hydaulic Desig of Sewes ad Stom Wate Dais Lectue 8 : Hydaulic Desig of Sewes ad Stom Wate Dais (Cotd.)

2 2 P age 7.9 Hydaulic Chaacteistics of Cicula Sewe Ruig Full o Patially Full D α d Figue 7.1 Sectio of a cicula sewe uig patially full a) Depth at Patial flow D D d cos (6) b) Theefoe popotioate depth d 1 1 cos D 2 2 (7) c) Popotioate aea a A 360 Si 2 d) Popotioate peimete: p P 360 (8) (9) e) Popotioate Hydaulic Mea Depth 360Si 1 R 2 (10) v f) Popotioate velocity = V R (11) I all above equatios except α eveythig is costat (Figue 7.1). Hece, fo diffeet values of α, all the popotioate elemets ca be easily calculated. These values of the hydaulic elemets ca be obtaied fom the popotioate gaph pepaed fo diffeet values

3 3 P age of d/d (Figue 7.2). The value of Maig s ca be cosideed costat fo all depths. I eality, it vaies with the depth of flow ad it may be cosideed vaiable with depth ad accodigly the hydaulic elemets values ca be ead fom the gaph fo diffeet depth atio of flow. Fom the plot it is evidet that the velocities i patially filled cicula sewe sectios ca exceed those i full sectio ad it is maximum at d/d of 0.8. Similaly, the dischage obtaied is ot maximum at flow full coditio, but it is maximum whe the depth is about 0.95 times the full depth. The sewes flowig with depths betwee 50% ad 80% full eed ot to be placed o steepe gadiets to be as self cleasig as sewes flowig full. The easo is that velocity ad dischage ae fuctio of tactive foce itesity which depeds upo fictio coefficiet as well as flow velocity geeated by gadiet of the sewe. Usig subscipt s deotig self cleasig equivalet to that obtaied i full sectio, the equied atios v s /V, q s /Q ad s s /S ca be computed as stated below: (a) Hydaulic elemets fo cicula sewe

4 4 P age (b) Hydaulic elemets of cicula sewe possessig equal selfcleasig popeties at all depths Figue 7.2 Popotioate gaph fo cicula sewe sectio (CPHEEO Maual, 1993) Coside a laye of sedimet of uit legth, uit width ad thickess t, is deposited at the ivet of the sewe (Figue 7.3). Let the slope of the sewe is θ degee with hoizotal. The dag foce o the itesity of tactive foce (ι) exeted by the flowig wate o a chael is give by: ι = γ w. R. S (12) Figue 7.3 A sedimet paticle movig o the sewe ivet Whee, γ w = uit weight of wate R = Hydaulic mea depth S = slope of the ivet of the sewe pe uit legth

5 5 P age With the assumptio that the quatity of tactive foce itesity at full flow ad patial flow implies equality of cleasig, i.e., fo sewes to be same self-cleasig at patial depth as full depth: ι = T Theefoe, γ w.. s s = γ w. R. S (13) Hece, s s = (R/) S O s s R S (14) Theefoe, vs V R s s S 1/ 2 (15) OR, by substitutig /R = S/s s v s V Ad q s Q R a A 1/ 6 R 1/ 6 (16) (17) Example: 2 A 300 mm diamete sewe is to flow at 0.3 depth o a gade esuig a degee of self cleasig equivalet to that obtaied at full depth at a velocity of 0.9 m/sec. Fid the equied gade ad associated velocity ad ate of dischage at this depth. Assume Maig s ugosity coefficiet = The vaiatio of with depth may be eglected. Solutio: Maig s fomula fo patial depth 1 v s 1/ 2 Fo full depth 1 1/ 2 V R S Usig V = 0.90 m/sec, = = ad R = D/4 = 75 mm = m / S

6 6 P age S = This is the gadiet equied fo full depth. ad, Q = A.V = π/4 (0.3) 2 x 0.90 = m 3 /s At depth d = 0.3D, (i.e., fo d/d = 0.3) we have a/a = ad /R = (eglectig vaiatio of ) ow fo the sewe to be same self cleasig at 0.3 m depth as it will be at full depth, we have the gadiet (s s ) equied as s s = (R/)S Theefoe, s s = S / = / = ow, the velocity v s geeated at this gadiet is give by v s V R 1/ 6 = 1 x (0.684) 1/6 x 0.9 = m/s The dischage q s is give by q s Q 1/ 6 a A R q s = 1 x (0.258) x (0.939) x (0.064) = m 3 /s Example: 3 A combied sewe was desiged to seve a aea of 60 sq. km with a aveage populatio desity of 185 pesos/hectae. The aveage ate of sewage flow is 350 L/Capita/day. The maximum flow is 50% i excess of the aveage sewage flow. The aifall equivalet of 12 mm i 24 h ca be cosideed fo desig, all of which is cotibutig to suface uoff. What will be the dischage i the sewe? Fid the diamete of the sewe if uig full at maximum dischage. Solutio: Total populatio of the aea = populatio desity x aea = 185 x 60 x 10 2 = 1110 x 10 3 pesos Aveage sewage flow = 350 x 11.1 x 10 5 Lites/day = x 10 6 L/day

7 7 P age = 4.5 m 3 /sec Stom wate flow = 60 x 10 6 x (12/1000) x [1/(24 x 60 x 60)] = 8.33 m 3 /sec Maximum sewage flow = 1.5 x aveage sewage flow = 1.5 x 4.5 = 6.75 m 3 /sec Total flow of the combied sewe = sewage flow + stom flow = = m 3 /sec Hece, the capacity of the sewe = m 3 /sec Hece, diamete of the sewe equied at the velocity of 0.9 m/s ca be calculated as π/4 (D) 2 x 0.90 = m 3 /s Hece, D = 4.62 m Example: 4 Fid the miimum velocity ad gadiet equied to taspot coase sad though a sewe of 40 cm diamete with sad paticles of 1.0 mm diamete ad specific gavity 2.65, ad ogaic matte of 5 mm aveage size with specific gavity 1.2. The fictio facto fo the sewe mateial may be assumed 0.03 ad oughess coefficiet of Coside k = 0.04 fo iogaic solids ad 0.06 fo ogaic solids. Solutio Miimum velocity i.e. self cleasig velocity Vs Vs 8k ( Ss 1) gd' f ' 8x0.04 (2.65 1) x9.81x = m/sec say 0.42 m/sec Similaly, fo ogaic solids this velocity will be m/sec Theefoe, the miimum velocity i sewe = 0.42 m/sec ow, Diamete of the sewe D = 0.4 m Hydaulic Mea Depth = D/4 = 0.4/4 = 0.1 m Usig Maig s fomula: V = 1/ R 2/3 S 1/ = (1/0.012) x (0.1) 2/3 x S 1/2

8 8 P age S = 1/ Theefoe, gadiet of the sewe equied is 1 i Example : 5 Desig a sewe uig 0.7 times full at maximum dischage fo a tow povided with the sepaate system, sevig a populatio 80,000 pesos. The wate supplied fom the wate woks to the tow is at a ate of 190 LPCD. The maig s = fo the pipe mateial ad pemissible slope is 1 i 600. Vaiatio of with depth may be eglected. Check fo miimum ad maximum velocity assumig miimum flow 1/3 of aveage flow ad maximum flow as 3 times the aveage. (fo d/d = 0.7, q/q = 0.838, v/v = 1.12) Solutio Aveage wate supplied = x 190 x (1/24 x 60 x 60 x 1000) = m 3 /sec Sewage poductio pe day, (cosideig 80% of wate supply) = x 0.8 = 0.14 m 3 /sec Maximum sewage dischage = 3 x 0.14 = 0.42 m 3 /sec ow fo d/d = 0.7, q/q = 0.838, v/v = 1.12 Theefoe, Q = 0.42/0.838 = 0.5 m 3 /sec ow 1 D Q 4 2 D 4 S 1/ D D 1 Q Theefoe, D = 0.78 m V = Q/A = 1.04 m/sec ow, v/v = 1.12 Theefoe v = 1.12 x 1.04 = 1.17 m/sec This velocity is less tha limitig velocity hece, OK Check fo miimum velocity ow q mi = 0.14/3 = m 3 /sec q mi /Q = 0.047/0.5 = 0.09 Fom popotioal chat, fo q/q = 0.09, d/d = 0.23 ad v/v = 0.65 Theefoe, the velocity at miimum flow = 0.65 x 1.04 = 0.68 m/sec This velocity is geate tha self cleasig velocity, hece OK d mi = 0.23 x 0.78 = 0.18 m 1/ 2

9 9 P age Commet: If the velocity at miimum flow is ot satisfactoy, icease the slope o ty with eductio i depth of flow at maximum dischage o eductio i diamete of the sewe. Assigmet: Solve the above poblem with populatio pesos ad pipe flowig 0.75 full at maximum dischage. The ate of wate supply is 150 LPCD, = 0.013, ad pemissible S = 1 i 600.