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Daniel Bernoulli (Groningen, 8 February 1700– Basel, 8 March 1782) was a Dutch-Swiss mathematician and was one of the many...
Henry Philibert Gaspard Darcy (June 10,1803 – January 3, 1858) wasa French engineer who made severalimportant contribution...
Antoine de Chézy (September 1, 1718– October 5, 1798) was a Frenchhydraulics engineer. He is known forthe Chézy formula, w...
CU06997 Fluid Dynamics Sewer calculation 12.1 Introduction (page 401) 12.2 Design of a simple pipe system (page 401-404) 1...
Energy loss [m]          • Turbulent flow                         • Friction loss (wrijvingsverlies)                      ...
Combined sewer / gemengd rioolstelsel                         Rain water       Rain                         Waste water   ...
Sewer    Location    Sewer    Overflow2
Chezy formula                                       𝑉= 𝐶∙        𝑅 ∙ 𝑆𝑓Chezy formula describes the mean velocity of unifor...
12𝑅Chezy coefficient                         𝐶 = 18 ∙ 𝑙𝑜𝑔                                                        𝑘    C=  ...
Surface roughness kS [m]                                             Equivalent Sand Roughness,                           ...
Head loss sewer pipe                                                                ∆𝐻    Combine         𝑉= 𝐶∙     𝑅 ∙ 𝑆𝑓...
Overflow                         Rain water       Rain                         Waste water      Waste                     ...
3Overflow / Weir                               𝑄= 𝑚∙ 𝐵∙           𝐻2                  Q=     discharge overflow           ...
Calculating sewer systems                         Rain           Rain                         Waste          Waste        ...
Question 1                     Rain          Rain                     Waste         Waste                                 ...
Question 2                      Rain=0           Rain=0                      Waste=10l/s      Waste=10l/s                 ...
Partially filled pipe                        𝑄 𝑝𝑎𝑟𝑡                 𝐼𝑛𝑝𝑢𝑡:        = 0,17                        𝑄 𝑓𝑢𝑙𝑙    ...
Table5
Question 3                     Rain=66 l/s       Rain=225 l/s                     Waste=10 l/s      Waste=10 l/s          ...
Question 3b                     Rain=66 l/s       Rain=225 l/s                     Waste=10 l/s      Waste=10 l/s         ...
Question 3c                  Rain=66 l/s      Rain=225 l/s                  Waste=10 l/s     Waste=10 l/s                 ...
Strategy [situation with overflow]PreparationInformation available for each pipe                12𝑅- Diameter, R, L, k, C ...
Strategy [situation with overflow]    Steps                        3                                             𝑄2     𝑄=...
Strategy [situation with overflow]    Remarks    • In manhole velocity is low so water level (y) ≈ total head (H)      Oth...
Question 3de                   Rain=66 l/s     Rain=225 l/s                   Waste=10 l/s    Waste=10 l/s                ...
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Cu06997 lecture 8_sewers

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Cu06997 lecture 8_sewers

  1. 1. Daniel Bernoulli (Groningen, 8 February 1700– Basel, 8 March 1782) was a Dutch-Swiss mathematician and was one of the manyprominent mathematicians in the Bernoullifamily. He is particularly remembered for hisapplications of mathematics to mechanics,especially fluid mechanics, and for hispioneering work in probability and statistics.Bernoullis work is still studied at length bymany schools of science throughout the world. 2 2 u uy1  z1   y 2  z2  1  H12 2 2g 2g0
  2. 2. Henry Philibert Gaspard Darcy (June 10,1803 – January 3, 1858) wasa French engineer who made severalimportant contributions to hydraulics. L u2 ΔΗ f     4 R 2gJulius Ludwig Weisbach (born 10 August 1806 inMittelschmiedeberg (now Mildenau), Erzgebirge,died 24 February 1871, Freiberg) was a Germanmathematician and engineer.0
  3. 3. Antoine de Chézy (September 1, 1718– October 5, 1798) was a Frenchhydraulics engineer. He is known forthe Chézy formula, which concernedthe velocity of pipe flow.[1] He diedin 1798 after being director of the Écolenationale des ponts et chaussées for lessthan a year.[2] His son was theorientalist Antoine-Léonard de Chézy. 𝑉= 𝐶∙ 𝑅 ∙ 𝑆𝑓http://chezy.sdsu.edu/0
  4. 4. CU06997 Fluid Dynamics Sewer calculation 12.1 Introduction (page 401) 12.2 Design of a simple pipe system (page 401-404) 12.3 Series, parallel and branched pipe systems (page 404-408) Reader : Sewer systems module for HPE (link on VLD) 5.4 Hydraulics1
  5. 5. Energy loss [m] • Turbulent flow • Friction loss (wrijvingsverlies) Total Head Pressure Head 2 2 L u u ΔΗ f       4 R 2g 2g Going to look at other formulas for calculating friction loss ΔH1 𝑉= 𝐶∙ 𝑅 ∙ 𝑆𝑓 𝑆𝑓 = 𝐿
  6. 6. Combined sewer / gemengd rioolstelsel Rain water Rain Waste water Waste GL (ground level) +6.00 m P4 P3 P2 P1 +5,5 m Ø500 concrete Ø300 PVC Ø250 PVC IL +4,00 m IL +3,90 m IL +3,73 m 50 m pump1 IL (Invert level) +3,53 m
  7. 7. Sewer Location Sewer Overflow2
  8. 8. Chezy formula 𝑉= 𝐶∙ 𝑅 ∙ 𝑆𝑓Chezy formula describes the mean velocity of uniform, turbulent flow 𝑉= Mean Fluid Velocity [m/s] Total Head R= Hydraulic Radius [m] Pressure Head 𝑆𝑓 = Hydraulic gradient [1] 8𝑔 𝐶= Chezy coefficient [m1/2/s] 𝜆 ΔH 𝑆𝑓 = 𝐿 ΔH3 Length
  9. 9. 12𝑅Chezy coefficient 𝐶 = 18 ∙ 𝑙𝑜𝑔 𝑘 C= Chezy coefficient [m1/2/s] R= Hydraulic Radius [m] kS = surface roughness [m]3
  10. 10. Surface roughness kS [m] Equivalent Sand Roughness, Material (ft) (mm) Copper, brass 1x10-4 - 3x10-3 3.05x10-2 - 0.9 Wrought iron, 1.5x10-4 - 8x10-3 4.6x10-2 - 2.4 steel Asphalt-lined 4x10-4 - 7x10-3 0.1 - 2.1 cast iron 3.3x10-4 - 1.5x10- Galvanized iron 2 0.102 - 4.6 Cast iron 8x10-4 - 1.8x10-2 0.2 - 5.5 Concrete 10-3 - 10-2 0.3 - 3.0 Uncoated Cast 7.4x10-4 0.226 Iron Coated Cast Iron 3.3x10-4 0.102 Coated Spun 1.8x10-4 5.6x10-2 Iron Cement 1.3x10-3 - 4x10-3 0.4 - 1.2s Wrought Iron 1.7x10-4 5x10-2 Uncoated Steel 9.2x10-5 2.8x10-2 Coated Steel 1.8x10-4 5.8x10-2 Wood Stave 6x10-4 - 3x10-3 0.2 - 0.9 PVC 5x10-6 1.5x10-3 Compiled from Lamont (1981), Moody (1944), and Mays (1999)3
  11. 11. Head loss sewer pipe ∆𝐻 Combine 𝑉= 𝐶∙ 𝑅 ∙ 𝑆𝑓 𝑄= 𝑉∙ 𝐴 𝑆𝑓 = 𝑖 = 𝐿 𝑄2 ∆𝐻 = 𝐿 2 𝐶 ∙ 𝑅ℎ ∙ 𝐴2 𝑠 ∆𝐻 = Head Loss, energy loss [m] Q = discharge pipe [m3/s] L= length of the pipe [m] C = Chezy coefficient [m1/2/s] R = Hydraulic Radius [m] A = Wetted Area, flow surface [m2]3 Sf ,i = slope of hydraulic gradient [-]
  12. 12. Overflow Rain water Rain Waste water Waste GL (ground level) +6.00 m P4 P3 P2 P1 +5,5 m Ø500 concrete Ø300 PVC Ø250 PVC IL +4,00 m IL +3,90 m IL +3,73 m 50 m pump4 IL (Invert level) +3,53 m
  13. 13. 3Overflow / Weir 𝑄= 𝑚∙ 𝐵∙ 𝐻2 Q= discharge overflow [m3/s] m= runoff coefficient (1,5 – 1,8) [m1/2/s] B= Width crest overflow [m] H= Head at overflow [m] measured from top crest!! Energy line In example m = 1,8 H4
  14. 14. Calculating sewer systems Rain Rain Waste Waste GL (ground level) +6.00 m P4 P3 P2 P1 +5,5 m Ø500 concrete Ø300 PVC Ø250 PVC IL +4,00 m IL +3,90 m IL +3,73 m 50 m pump5 IL (Invert level) +3,53 m
  15. 15. Question 1 Rain Rain Waste Waste GL +6.00 m +5,5 m P4 P3 P2 P1 Ø500 concrete Ø300 PVC Ø250 PVC IL +4,00 m IL +3,90 m IL +3,73 m 50 m Pump5 IL +3,53 m
  16. 16. Question 2 Rain=0 Rain=0 Waste=10l/s Waste=10l/s GL +6.00 m +5,5 m P4 P3 P2 P1 Ø500 concrete Q=10 l/s Q=20 l/s Ø300 PVC Ø250 PVC IL +4,00 m IL +3,90 m IL +3,73 m 50 m Pump5 IL +3,53 m
  17. 17. Partially filled pipe 𝑄 𝑝𝑎𝑟𝑡 𝐼𝑛𝑝𝑢𝑡: = 0,17 𝑄 𝑓𝑢𝑙𝑙 𝑢 𝑝𝑎𝑟𝑡 𝑂𝑢𝑡𝑝𝑢𝑡: = 0,75 𝑢 𝑓𝑢𝑙𝑙 ℎ𝑂𝑢𝑡𝑝𝑢𝑡: = 0,27 𝐷5
  18. 18. Table5
  19. 19. Question 3 Rain=66 l/s Rain=225 l/s Waste=10 l/s Waste=10 l/s GL +6.00 m P4 P3 P2 P1 +5,5 m Ø500 concrete Ø300 PVC Ø250 PVC IL +4,00 m IL +3,90 m IL +3,73 m 50 m Pump=20 l/s5 IL +3,53 m
  20. 20. Question 3b Rain=66 l/s Rain=225 l/s Waste=10 l/s Waste=10 l/s GL +6.00 m P1 P4 P3 P2 +5,5 m Ø500 beton Ø300 PVC Ø250 PVC IL +4,00 m IL +3,90 m IL +3,73 m 50 m Pump=20 l/s5 IL +3,53 m
  21. 21. Question 3c Rain=66 l/s Rain=225 l/s Waste=10 l/s Waste=10 l/s GL +6.00 m +5,5 m P4 P3 P2 Ø500 beton Ø300 PVC P1 Ø250 PVC Q=291 l/s Q=66 l/s 50 m Pump=20 l/s5 In example m = 1,8
  22. 22. Strategy [situation with overflow]PreparationInformation available for each pipe 12𝑅- Diameter, R, L, k, C 𝐶 = 18 ∙ 𝑙𝑜𝑔- Discharge and Velocity 𝑘Information Overflow / weir- Width, m- Discharge- Level crest in m N.A.P.5
  23. 23. Strategy [situation with overflow] Steps 3 𝑄2 𝑄= 𝑚∙ 𝐵∙ 𝐻2 ∆𝐻 = 𝐿 2 𝐶 ∙ 𝑅ℎ ∙ 𝐴2 𝑠 All levels in m N.A.P. 1. Calculate H at weir 2. Calculate ∆H each pipe 3. Water level at weir (P1) = level crest weir + H at weir 4. Water level at P2 = Water level at weir + ∆Hweir(p1) – p2 5. Water level at P3 = Water level at P2 + ∆H p2– p3 6. Water level at P4 = Water level at P3 + ∆H p3– p45
  24. 24. Strategy [situation with overflow] Remarks • In manhole velocity is low so water level (y) ≈ total head (H) Otherwise you have to take the velocity head (u2/2g) into account • Pipes are submerged • Steady situation • Turbulent flow • Subcritical flow [stromend] (discussed later, most of the time flow is subcritical With subcritical flow [stromend] the downstream situation affects the upstream situation. So that is why you start at the weir and work back to P3.5
  25. 25. Question 3de Rain=66 l/s Rain=225 l/s Waste=10 l/s Waste=10 l/s GL +6.00 m +5,5 m P4 P3 P2 Q=0 l/s Ø500 beton v=0 m/s P1 Ø300 PVC I=0 Ø250 PVC Q=291 l/s Q=66 l/s v=1,48 m/s v=0,93 m/s I=1:166 Pump=20 l/s I=1:2445 50 m In example m = 1,8

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