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- 1. Daniel Bernoulli (Groningen, 8 February 1700 – Basel, 8 March 1782) was a Dutch- Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world. 2 2 u u y1 z1 y 2 z2 1 H12 2 2g 2g 0
- 2. Henry Philibert Gaspard Darcy (June 10, 1803 – January 3, 1858) was a French engineer who made several important contributions to hydraulics. L u2 ΔΗ f 4 R 2g Julius Ludwig Weisbach (born 10 August 1806 in Mittelschmiedeberg (now Mildenau), Erzgebirge, died 24 February 1871, Freiberg) was a German mathematician and engineer. 0
- 3. Antoine de Chézy (September 1, 1718 – October 5, 1798) was a French hydraulics engineer. He is known for the Chézy formula, which concerned the velocity of pipe flow.[1] He died in 1798 after being director of the École nationale des ponts et chaussées for less than a year.[2] His son was the orientalist Antoine-Léonard de Chézy. 𝑉= 𝐶∙ 𝑅 ∙ 𝑆𝑓 http://chezy.sdsu.edu/ 0
- 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 Hydraulics 1
- 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 ΔH 1 𝑉= 𝐶∙ 𝑅 ∙ 𝑆𝑓 𝑆𝑓 = 𝐿
- 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 pump 1 IL (Invert level) +3,53 m
- 7. Sewer Location Sewer Overflow 2
- 8. Chezy formula 𝑉= 𝐶∙ 𝑅 ∙ 𝑆𝑓 Chezy 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 ΔH 3 Length
- 9. 12𝑅 Chezy coefficient 𝐶 = 18 ∙ 𝑙𝑜𝑔 𝑘 C= Chezy coefficient [m1/2/s] R= Hydraulic Radius [m] kS = surface roughness [m] 3
- 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. 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. 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 pump 4 IL (Invert level) +3,53 m
- 13. 3 Overflow / 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 H 4
- 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 pump 5 IL (Invert level) +3,53 m
- 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 Pump 5 IL +3,53 m
- 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 Pump 5 IL +3,53 m
- 17. Partially filled pipe 𝑄 𝑝𝑎𝑟𝑡 𝐼𝑛𝑝𝑢𝑡: = 0,17 𝑄 𝑓𝑢𝑙𝑙 𝑢 𝑝𝑎𝑟𝑡 𝑂𝑢𝑡𝑝𝑢𝑡: = 0,75 𝑢 𝑓𝑢𝑙𝑙 ℎ 𝑂𝑢𝑡𝑝𝑢𝑡: = 0,27 𝐷 5
- 18. Table 5
- 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/s 5 IL +3,53 m
- 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/s 5 IL +3,53 m
- 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/s 5 In example m = 1,8
- 22. Strategy [situation with overflow] Preparation Information available for each pipe 12𝑅 - Diameter, R, L, k, C 𝐶 = 18 ∙ 𝑙𝑜𝑔 - Discharge and Velocity 𝑘 Information Overflow / weir - Width, m - Discharge - Level crest in m N.A.P. 5
- 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– p4 5
- 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. 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=1:244 5 50 m In example m = 1,8