DVC Calculus Field Trip Carollo Engineers. Dan Frost Rob Hunt. April 28 th , 2011. Field Trip Outline. Introduction of speakers (9:30-9:35) Introduction to Carollo (9:35-9:50) Office Tour (9:50-10:10) Calculus at Carollo and Snack (10:20-10:40) Questions (10:40-11:00). Dan Frost.
DVC Calculus Field Trip Carollo Engineers Dan Frost Rob Hunt April 28th, 2011
Field Trip Outline • Introduction of speakers (9:30-9:35) • Introduction to Carollo (9:35-9:50) • Office Tour (9:50-10:10) • Calculus at Carollo and Snack (10:20-10:40) • Questions (10:40-11:00)
Dan Frost • BS/MS Env. Eng. from Cal Poly in 2008 • Carollo Engineers since 2008 • Experience Highlights: • Wastewater Rehab Projects – Fresno & DSRSD • Napa Wastewater Master Plan • City of San Leandro WPCP Rehabilitation Project • City of Stockton CIP and Energy Management Plan • Algae to Biofuels
Rob Hunt • BS Civil Eng. from UC Davis in 2002 • MS Civil & Env. Eng. from UC Davis in 2004 • Carollo Engineers since 2004 • Experience Highlights: • City of Davis Master Plan and Preliminary Design • West County Wastewater District Connection Fee/Rate Study and Preliminary Design • City of Modesto Wastewater Treatment Plant Design • City of South San Francisco Wet Weather Pump Station Design and Construction
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.
Carollo Statistics • Founded 1933 • 630+ employees • 300+ professional engineers • Multi disciplined • Sanitary/environmental • Structural • Mechanical • Electrical • Instrumentation • Civil • Chemical
Company Organization CEO Partners Associates Engineers Drafters Graphics Document Processing Business Development Human Resources
Key drivers for water and wastewater projects include: • Growth • Regulations • Aging Infrastructure • Management/Public Policy
Wastewater Treatment Plant No. 1 Fountain Valley, CA Orange County Sanitation Districts Orange County, CA360 mgd (combined) Reclamation Plant No. 2 Huntington Beach, CA
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.ppt14
Clark County Water Reclamation District, NV130-mgd of biological phosphorus removal
What do we produce for our clients? • Proposals and Statements of Qualifications • Preliminary studies and reports • Master plans • Design plans and specifications
Office Tour • Library and Central Files • Engineering Groups • Civil/Process • Structural • Electrical and Instrumentation • Mechanical • Graphics • Business Development • Drafting • ISG/Tech Support
Calculus at Carollo • Do we use it? • How do we use it? • Hydraulic calculations • Volume calculations • Structural analysis • Questions?
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
Derivation of the Bernoulli Equation • Start with Newton’s Second Law…. Bernoulli’s Equation
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
Applications of the Bernoulli Equation Determining flow from a tank or reservoir
Applications of the Bernoulli Equation Sizing and designing culverts
Applications of the Bernoulli Equation Sizing pumps and pipelines
Applications of the Bernoulli Equation Determining the flow, pressure, and headloss at points within a parallel pipe system
Calculating flow volumes from hydrographs • Hydrograph - flow vs. time (e.g. storm, river) • Volume of water over time = Area under curve
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
Hydrograph Example • Receive raw data from client
Hydrograph Example • Receive raw data from client
Hydrograph Example • Graph raw data
Hydrograph Example • Volume due to Rainfall (I&I) = Area btw Curves • Integrate equation for curves
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
Hydrograph Example • Volume due to Rainfall (I&I) = Area btw Curves • Approximation (Avg. End Area Method)
Hydrograph Example • Approximation: 1,252 Gallons
Position, Velocity, and Acceleration • x = x0 + v0t + ½ at2 (meters, m) • v = dx/dt = 0 + v0 + at (meters/second, m/s) • a = dv/dt = 0 + 0 + a (meters/second/second, m/s2)
Projectile Motion • y = y0 + vy0t + ½ (ay)t2 • ay = -g = -9.8 m/s2 • x = x0 + vx0t + ½ (ax)t2 • ax = 0 y x
Software used to analyze complex systems • Hydraulix • BioTran/BioWin • EnerCalc • STAAD
Structural Analysis • Structural engineers use calculus to determine the maximum stress of structural elements under different loads.
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.
Structural Analysis • Step 1: Determine all forces using plane static equilibrium equations.
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.
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.