lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

DVC Calculus Field TripCarollo Engineers

November 15th, 2010

Dan Frost

Katy Rogers

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

Field Trip Outline

• Introduction of speakers

• Introduction to Carollo

• Office tour

• Calculus at Carollo and lunch

• Questions

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/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.

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/6

Carollo Statistics

• Founded 1933• 630+ employees• 300+ professional engineers• Multi disciplined

- Sanitary/environmental- Structural- Mechanical- Electrical- Instrumentation- Civil- Chemical

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/7

Company Organization

CEO

Partners

Associates

EngineersDraftersGraphics

Document ProcessingBusiness Development

Human Resources

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/8

Carollo currently maintains 32 offices in 12 states

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/9

What types of projects do we work on?

• Water treatment

• Wastewater treatment

• Infrastructure

• Research and Development

• Water Reuse

• Construction Management

• Integrated Water Resources

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

0

Key drivers for water and wastewater projects include:

• Growth

• Regulations

• Aging Infrastructure

• Management/Public Policy

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

1

Project Examples….

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

2

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

Reclamation Plant No. 2Huntington Beach, CA

Wastewater Treatment Plant No. 1Fountain Valley, CA

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

3 City of Stockton, CAWestside Sewer Interceptor41,000 LF/72 inch pipe

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

GCDCorpOv903.ppt13

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

5 Napa Sanitation District, CA10-mgd DynaSand filter for reuse

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

6

Stockton WWTP Facility Aerial

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

7

What do we produce for our clients?

• Proposals and Statements of Qualifications

• Preliminary studies and reports

• Master plans

• Design plans and specifications

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

8

Office Tour

• Library and Central Files

• Engineering groups- Civil/Process

- Structural

- Electrical and instrumentation

- Mechanical

• Graphics

• Business development

• Drafting

• ISG/Tech Support

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/1

9

Calculus at Carollo

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

0

Calculus at Carollo

• Do we use it?

• How do we use it?- Hydraulic calculations

- Volume calculations

- Structural analysis

• Questions?

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

1

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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

2

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)

b

a

dx)]x(g)x(f[A x)YY(2

1A 21

XkX)SK

S(VXQ d

s

moo

WWewo XQX)QQ(

21111111 QQVApVAp 0

V V V V

dMu dV dV u dV u dV

dt t t

02

1

2

1

2

1 gdzVdV

dp

kCdt

dCR

o

C

C

Ro

o

CC

Clnk

b2bb

a2aa

ghv2

1P

ghv2

1P

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

3

• Start with Newton’s Second Law….

Derivation of the Bernoulli Equation

Bernoulli’s Equation

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

4

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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

5

Applications of the Bernoulli Equation

Determining flow from a tank or reservoir

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

6

Applications of the Bernoulli Equation

Sizing and designing culverts

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

7

Applications of the Bernoulli Equation

Sizing pumps and pipelines

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

8

Applications of the Bernoulli Equation

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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/2

9

Hydraulic Profile for the City of Modesto WWTP

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

0

Calculating flow volumes from hydrographs

• Hydrograph - flow vs. time (e.g. storm, river)

• Volume of water over time = Area under curve

Time

Flo

w

Time

Flo

w

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

1

• 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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

2

Hydrograph Example

• Receive raw data from client

Treatment 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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

3

Hydrograph Example

• Receive raw data from client

Treatment 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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

4

Hydrograph Example

• Graph raw data

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

20

40

60

80

100

120

140

160

180

Flow from Rainfall = f(x)

Base Flow = g(x)

Time (Hours)

Flo

w (

gal/hr)

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

5

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

20

40

60

80

100

120

140

160

180

Flow from Rainfall = f(x)

Base Flow = g(x)

Time (Hours)

Flo

w (

gal/hr)

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

6

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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

7

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

20

40

60

80

100

120

140

160

180

Flow from Rainfall = f(x)

Base Flow = g(x)

Time (Hours)

Flo

w (

gal/hr)

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

8

Hydrograph Example

• Approximation: 1,252 Gallons

Time FlowAvg

Flow Duration Volume

t QQ

(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

t QQ

(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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/3

9

Structural Analysis

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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

0

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.

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

1

Structural Analysis

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

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

2

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.

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

3

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.

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

4

Structural Analysis

• In summary….

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

5

Another example….

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

6

More examples….

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

7

Software used to analyze complex systems

• Hydraulix

• BioTran/BioWin

• EnerCalc

• STAAD

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

8

Questions?

lh10

10re

crui

tmen

t-ca

lpol

y.pp

tx/4

9

End of Presentation