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November 15 th , 2010

DVC Calculus Field Trip Carollo Engineers. Dan Frost Katy Rogers. November 15 th , 2010. Field Trip Outline. Introduction of speakers Introduction to Carollo Office tour Calculus at Carollo and lunch Questions. Dan Frost. BS/MS Env. Eng. from Cal Poly in 2008

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November 15 th , 2010

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  1. DVC Calculus Field Trip Carollo Engineers Dan Frost Katy Rogers November 15th, 2010

  2. Field Trip Outline • Introduction of speakers • Introduction to Carollo • Office tour • Calculus at Carollo and lunch • Questions

  3. Dan Frost • BS/MS Env. Eng. from Cal Poly in 2008 • Carollo Engineers since 2008 • Experience Highlights: • Digester Rehab/FOG Facilities – Fresno & DSRSD • Napa Wastewater Master Plan • City of San Leandro WPCP Rehabilitation Project • City of Stockton CIP and Energy Management Plan • Algae to Biofuels

  4. Katy Rogers • BS Civil Eng. from UC Davis in 2007 • MS Env. Eng. from Stanford in 2008 • Carollo Engineers since 2008 • Experience Highlights: • City of Modesto Tertiary Wastewater Treatment Plant • City of Modesto Engineer’s Report • City of Turlock THM Study • City of San Francisco CIP

  5. Introduction to Carollo Engineers • We are the largest firm in the United States dedicated solely to water and wastewater treatment. • Carollo Engineers provides planning, design, and construction management services for municipal clients.

  6. Carollo Statistics • Founded 1933 • 630+ employees • 300+ professional engineers • Multi disciplined • Sanitary/environmental • Structural • Mechanical • Electrical • Instrumentation • Civil • Chemical

  7. Company Organization CEO Partners Associates Engineers Drafters Graphics Document Processing Business Development Human Resources

  8. Carollo currently maintains 32 offices in 12 states

  9. What types of projects do we work on? • Water treatment • Wastewater treatment • Infrastructure • Research and Development • Water Reuse • Construction Management • Integrated Water Resources

  10. Key drivers for water and wastewater projects include: • Growth • Regulations • Aging Infrastructure • Management/Public Policy

  11. Project Examples….

  12. Wastewater Treatment Plant No. 1 Fountain Valley, CA Orange County Sanitation Districts Orange County, CA360 mgd (combined) Reclamation Plant No. 2 Huntington Beach, CA

  13. City of Phoenix, AZ Southern Avenue Interceptor 160,000 LF/48-90 inch pipes City of Stockton, CA Westside Sewer Interceptor 41,000 LF/72 inch pipe GCDCorpOv903.ppt13

  14. Clark County Water Reclamation District, NV130-mgd of biological phosphorus removal

  15. Napa Sanitation District, CA10-mgd DynaSand filter for reuse

  16. Stockton WWTP Facility Aerial

  17. What do we produce for our clients? • Proposals and Statements of Qualifications • Preliminary studies and reports • Master plans • Design plans and specifications

  18. Office Tour • Library and Central Files • Engineering groups • Civil/Process • Structural • Electrical and instrumentation • Mechanical • Graphics • Business development • Drafting • ISG/Tech Support

  19. Calculus at Carollo

  20. Calculus at Carollo • Do we use it? • How do we use it? • Hydraulic calculations • Volume calculations • Structural analysis • Questions?

  21. Do we use calculus at Carollo? • Short Answer: Yes • Long Answer: • We use simple calculus-derived equations • We also use software to solve several equations simultaneously

  22. Algebraic equations derived from calculus:

  23. Derivation of the Bernoulli Equation • Start with Newton’s Second Law…. Bernoulli’s Equation

  24. How we use the Bernoulli Equation at Carollo: • To determine pressure, velocity, and elevation at points within a hydraulic system • To size pipes, valves, pumps, and turbines • To determine headloss through a pipe due to friction and connections • To develop hydraulic profiles

  25. Applications of the Bernoulli Equation Determining flow from a tank or reservoir

  26. Applications of the Bernoulli Equation Sizing and designing culverts

  27. Applications of the Bernoulli Equation Sizing pumps and pipelines

  28. Applications of the Bernoulli Equation Determining the flow, pressure, and headloss at points within a parallel pipe system

  29. Hydraulic Profile for the City of Modesto WWTP

  30. Calculating flow volumes from hydrographs • Hydrograph - flow vs. time (e.g. storm, river) • Volume of water over time = Area under curve

  31. Calculating flow volumes from hydrographs • Estimate volume of water from a rainfall event • Size culverts, pipelines • Wastewater storage • Actual data not defined by simple equations • Apply approximation methods • Trapezoidal Rule: A = Δx(yo/2 + y1 + y2 + yn/2) • Average End Area Method: A = ½ (y1+y2) * Δx

  32. Hydrograph Example • Receive raw data from client

  33. Hydrograph Example • Receive raw data from client

  34. Hydrograph Example • Graph raw data

  35. Hydrograph Example • Volume due to Rainfall (I&I) = Area btw Curves • Integrate equation for curves

  36. Hydrograph Example • Integration of f(t): • Q = Flow During Rain Event = f(t) = -(2t)2 + 50t + 5 •  f(t) =  (-(2t)2 + 50t + 5)dt = -4/3t3 + 25t2 +5t + C • At t = 0, Q = 5 => C = 5 • From t = 0 to t = 12 => [-4/3(12)3 + 25(12)2 +5(12) + 5] - [-4/3(0)3 + 25(0)2 +5(0) + 5] = 1,356 gallons • Integration of g(t): • Q = Typical Flow = g(t) = 0.5t+5 •  g(t) =  (0.5t+5)dt = 1/4t2 + 5t + C • At t = 0, Q = 5 => C = 5 • From t = 0 to t = 12 => [1/4(12)2 + 5(12) + 5] – 5 = 96 gallons • Total Flow Due to Rainfall = 1,356 – 96 = 1,260 gallons

  37. Hydrograph Example • Volume due to Rainfall (I&I) = Area btw Curves • Approximation (Avg. End Area Method)

  38. Hydrograph Example • Approximation: 1,252 Gallons

  39. Structural Analysis • Structural engineers use calculus to determine the maximum stress of structural elements under different loads.

  40. Structural Analysis • Shear at a point is the sum of all vertical forces acting on an object. • Moment at a point is the total bending moment acting on an object.

  41. Structural Analysis • Step 1: Determine all forces using plane static equilibrium equations.

  42. Structural Analysis • Step 2: Calculate shear at a point by integrating the load function w(x) or the area under the load diagram up to that point.

  43. Structural Analysis • Step 3: Calculate moment at a point by integrating the shear function V(x) or the area under the shear diagram up to that point.

  44. Structural Analysis • In summary….

  45. Another example….

  46. More examples….

  47. Software used to analyze complex systems • Hydraulix • BioTran/BioWin • EnerCalc • STAAD

  48. Questions?

  49. End of Presentation

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