November 15 th , 2010

DVC Calculus Field TripCarollo Engineers

November 15th, 2010

Dan FrostKaty Rogers

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• 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

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

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

Partners

Associates

EngineersDraftersGraphics

Document ProcessingBusiness Development

Human Resources

Carollo currently maintains 32 offices in 12 states

What types of projects do we work on?

• Water treatment• Wastewater treatment• Infrastructure • Research and Development• Water Reuse• Construction Management• Integrated Water Resources

Key drivers for water and wastewater projects include:

• Growth• Regulations• Aging Infrastructure• Management/Public Policy

Project Examples….

Orange County Sanitation Districts Orange County, CA360 mgd (combined)

Reclamation Plant No. 2Huntington Beach, CA

Wastewater Treatment Plant No. 1Fountain Valley, CA

x/13 City of Stockton, CA

Westside Sewer Interceptor41,000 LF/72 inch pipe

City of Phoenix, AZSouthern Avenue Interceptor160,000 LF/48-90 inch pipes

GCDCorpOv903.ppt13

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

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

Stockton WWTP Facility Aerial

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

Algebraic equations derived from calculus:Calculus Algebra Used For:

Area under a curve Calculating rain volume, excavation volume, etc

Conservation of Mass Mass and flow balances (calculating flows and masses when multiple streams are involved)

Conservation of Energy Hydraulic design (structures, pipes, pumps, valves, etc), Hydraulic Profiles

Rate Equation Treatment design (reaction time)

dx)]x(g)x(f[A x)YY(21A 21

XkX)SK

S(VXQ ds

WWewo XQX)QQ(

21111111 QQVApVAp 0

V V V V

dM u dV dV u dV u dVdt t t

1 gdzVdVdp

kCdtdCR

CCClnk

ghv21P

• Start with Newton’s Second Law….

Derivation of the Bernoulli Equation

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

Sizing and designing culverts

Sizing pumps and pipelines

Determining the flow, pressure, and headloss at points within a parallel pipe system

Hydraulic Profile for the City of Modesto WWTP

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

• 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

Calculating flow volumes from hydrographs

Hydrograph Example

• Receive raw data from clientTreatment Plant Flow during Rainfall Event Typical Treatment Plant Flow

Time Flow Time Flowt Q t Q0 5 0 51 51 1 5.52 89 2 63 119 3 6.54 141 4 75 155 5 7.56 161 6 87 159 7 8.58 149 8 99 131 9 9.5

10 105 10 1011 71 11 10.512 29 12 11

Hydrograph Example

• Receive raw data from clientTreatment Plant Flow during Rainfall Event Typical Treatment Plant Flow

Time Flow f(x) = f(t) = Q = -2t2+ 50t + 5 Time Flow g(x) = g(t) = Q = 0.5t+5t Q t Q0 5 0 51 51 1 5.52 89 2 63 119 3 6.54 141 4 75 155 5 7.56 161 6 87 159 7 8.58 149 8 99 131 9 9.5

10 105 10 1011 71 11 10.512 29 12 11

Hydrograph Example

• Graph raw data

0 1 2 3 4 5 6 7 8 9 10 11 120

180Flow from Rainfall = f(x)Base Flow = g(x)

Time (Hours)

Hydrograph Example

• Volume due to Rainfall (I&I) = Area btw Curves- Integrate equation for curves

0 1 2 3 4 5 6 7 8 9 10 11 120

Time (Hours)

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)

0 1 2 3 4 5 6 7 8 9 10 11 120

Time (Hours)

Hydrograph Example

• Approximation: 1,252 Gallons

Time FlowAvg

Flow Duration Volume

(gal/hr) t (Hrs) gal0 51 5.5 5.25 1 5.252 6 5.75 1 5.753 6.5 6.25 1 6.254 7 6.75 1 6.755 7.5 7.25 1 7.256 8 7.75 1 7.757 8.5 8.25 1 8.258 9 8.75 1 8.759 9.5 9.25 1 9.25

10 10 9.75 1 9.7511 10.5 10.25 1 10.2512 11 10.75 1 10.75

Sum = 96

Time FlowAvg

Flow Duration Volume

(gal/hr) t (Hrs) gal0 51 51 28 1 282 89 70 1 703 119 104 1 1044 141 130 1 1305 155 148 1 1486 161 158 1 1587 159 160 1 1608 149 154 1 1549 131 140 1 140

10 105 118 1 11811 71 88 1 8812 29 50 1 50

Sum = 1,348

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.

Structural Analysis• In summary….

Another example….

More examples….

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

Questions?

End of Presentation

November 15 th , 2010

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Lecture 19 November 16 th 2010

Actuarial Placements the-arc.co.uk 11 th November 2010

Resident’s Briefing November 20 th, 2010

CIQ Workshop November 30 th – December 1 st 2010

Finance & Accounting Cornell University November 16 th, 2010

15 th and 16 th November 2010 Orange Civic Theatre

Teach First 15 th November 2010

12 th November 2010

Wates & Social Enterprise Finditinbirmingham – 4 th November 2010

Sustainable Urban Development – (SUD) WEBCOG – 4 th November 2010

Monday November 8 th , 2010

Castellanza, 10 th November, 2010

KAZAKHSTAN Presented by: Vladimir Stepanov November 10 th 2010

Friday Sermon November 19 TH , 2010

Disability Support Service CIT November 4 th, 2010

NCEOD Report Launch November 11 th 2010 John MacFie

Information Webinar 5 th November 2010

Regional Representatives 10 th November 2010 Consultant Job Planning Regional Representatives 10 th November 2010 Graham Venn

23 th November 2010