Exponential Loading W(t)=W e e e t W e = 1625 kg/d e = 0.04558 - - PDF document

CEE 577 Lecture #6 9/25/2017 1

Lecture #6 (particular solutions, cont.)

David A. Reckhow CEE 577 #6 1

Chapra L4 (cont.)

Updated: 25 September 2017

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Exponential Loading

 W(t)=Weeet

 We= 1625 kg/d  e= 0.04558 /yr David A. Reckhow CEE 577 #6 2

0.5 1 1.5 2 2.5 3 5 10 15 20 25 Time (years) Concentration (mg/L)

) ( ) (

t t e e p

e e V W c

e

 

 



  

200000 400000 600000 800000 1000000 1200000

• 2

2 4 6 8 10 12 Loading (Kg/y) Time (years) Expon

CEE 577 Lecture #6 9/25/2017 2

Sinusoidal Loading

 W(t)=W‐bar+ Wasin(t‐)

 W‐bar= 500,000 kg/yr  Wa = 250,000 kg/yr  Tp = 2 = 1 yr  phase shift,  = (0.25)2=0.5 David A. Reckhow CEE 577 #6 3

100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000

• 1
• 0.5

0.5 1 1.5 2 Time (years) Loading (Kg/y)

Wa  W-bar Tp

200000 400000 600000 800000 1000000 1200000

• 2

2 4 6 8 10 12 Time (years) Loading (Kg/y) Sinusoid

Sinusoidal Loading

0.2 0.4 0.6 0.8 1 1.2 5 10 15 20 25 Time (years) Concentration (mg/L)

David A. Reckhow CEE 577 #6 4

   

) exp( ) ( sin ) ( sin ) 1 (

2 2 2 2

t V W t V W e V W c

a a t p

            



          



W-bar= 500,000 kg/yr Wa = 250,000 kg/yr Tp = 2 = 1 year phase shift ,  = 0.5

Return

           arctan ) (

Response phase shift

CEE 577 Lecture #6 9/25/2017 3

Sinusoidal Loading

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k   0 042  . k   0 0003 015 . .  k   0 001 0 42 . .  k   0 005 187 . . 

Increasing 

Q=2x105 m3/d A=1.1x108 m2 V=1.75x109 3

Example (similar to: 11.1 from Reckhow & Chapra)

 Green Lake & Happy Valley

 Hydraulic Parameters

 Q=20x106 m3/yr, V=100x106 m2, As=10x106 m2, H=10m

 Decay: k=1.05/yr  Loading

 local WWTP: 0.115x104 g/capita/yr, 20,000 people (long term,

but at t=0, WW is pumped to regional plant)

 new paper mill: 50x106g/yr  new cattle feed lot: 150 animals, increasing by 100 cattle each

year, 0.1x106 g/animal

 New scenario: regional WWTP cannot accept new WW, town of

Happy Valley is growing exponentially at 0.3/yr

 New canning plant: annual cycle, avg=30x106 g/yr

 max on Oct 1; min on Apr 1 (half of average) David A. Reckhow CEE 577 #6 6

CEE 577 Lecture #6 9/25/2017 4

Summation of Loading

0.5 1 1.5 2 2.5 3 3.5 4 5 10 15 20 25 Time (years) Concentration (mg/L)

David A. Reckhow CEE 577 #6 7

Canning plant

Decay of Co WWTP Cattle Feed Lot Paper Mill Summation

WWTP: dirunal variations

 Figures 1.6 a & b, from Thomann & Mueller

David A. Reckhow CEE 577 #6 8

CEE 577 Lecture #6 9/25/2017 5

WWTP: weekly variations

 Figure 1.6 c, from Thomann & Mueller

David A. Reckhow CEE 577 #6 9

WWTP: Seasonal Variations

 Figure 1.6 d, from Thomann & Mueller

David A. Reckhow CEE 577 #6 10

CEE 577 Lecture #6 9/25/2017 6

Next: Cultural Eutrophication

 Many correlated WQ problems

 Floating mats of algae  Low DO  High P?

David A. Reckhow CEE 577 #6 11

 To next lecture

David A. Reckhow CEE 577 #6 12