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DO Sag Curve (Streeter-Phelps) - April 17, 2006

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DO Sag Curve Streeter-Phelps

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Do sag curve streeter phelps l.jpg

DO Sag Curve (Streeter-Phelps)

April 17, 2006

Objectives l.jpg


  • Draw and discuss the DO sag curve

  • Calculate DO and solve for a variety of unknowns using the DO sag equation

Biota vs d o l.jpg

Biota vs. D.O.

Slide4 l.jpg

Typical DO sag curve

Initial Deficit (Da)






Saturation DO (Dos)




Dissolved Oxygen (mg/L)

DO Concentration (DO)


2 4 6 8 10

Travel Time (d)

What we re trying to accomplish and how we re going to do it l.jpg

What we’re trying to accomplishand how we’re going to do it

  • Calculate the dissolved oxygen deficit using mass balance equation

  • Start with simplified model and calculation

    • BOD

    • Reaeration

    • Initial DO reduction

  • Add some more components to the model

  • Get an equation for D (dissolved oxygen deficit)

  • Get an equation for tc, the “critical time” when the dissolved oxygen is at its lowest point

Very simplified model l.jpg

Very Simplified Model

  • Assume plug-flow and define the control volume as a unit rectangle

  • Follow the movement of the plug which tracks the pollution downstream

  • Determine the initial oxygen content after mixing (La)

Mass balance for initial condition l.jpg

Mass-Balance for Initial Condition

Qr, Lr, Tr

Qa, La, Tf (Ta)

Qw, Lw, Tw

Account for other do gain loss processes l.jpg

Account for other DO gain/loss processes



Qr, Lr, Tr

Qa, La, Tf (Ta)

Qw, Lw, Tw

Why we do all of this l.jpg

Why We Do All of This

  • To determine how much waste can safely be put in a river

  • Process

    • Determine minimum acceptable DO

    • Calculate waste load that keeps critical DO above the minimum

  • If discharged waste is above acceptable limits:

    • More treatment needed

    • Discharger may add dissolved oxygen to wastewater

  • Cautions

    • Be sure to make calculations for worst conditions

    • Remember to consider all dischargers