The do sag curve and the streeter phelps equation

1. The DO Sag Curve and the
Streeter-Phelps Equation
Submitted to-
Dr. Anju Malik
Submitted By-
Keshav
Roll no. 07
M.Sc. (F)

2. Dissolved oxygen
The amount of gaseous oxygen dissolved in
water . Oxygen enters the water by direct
absorption of from the atmosphere by rapid
movement or as waste product of
photosynthesis.

3. BALANCE
ORGANIC MATTER (C, N) DECAY
SEDIMENT DEMAND
RESPIRATION
ATMOSPHERIC DIFFUSION
PHOTOSYNTHESIS
TRIBUTARIES
TRIBUTARIES
SOURCES
SINKS

4. SHINK
RESPIRATION BOD

5. FACTOR’S
AFFECTING DO
TEMPERATURE
SALINITY
ELEVATION

6.  One of the earliest mathematical water quality models was developed by for
the Ohio River by H.S.Streeter and E.B. Phelps in 1925. Hence the model
is referred to as the Streeter-Phelps model.
 The Streeter-Phelps equation accurately models the amount of DO in a
stream after wastewater is discharge into it.
 The DO sag curve represents how the DO concentration in a volume of
water changes over time or distance after organic material is introduced.
This curve is calculated by the Streeter-Phelps equation
 The plot of the DO as a function of time is called the DO sag curve.
 This changing concentration of DO in a river after the introduction of
organic material is called the DO sag curve.

7. The oxygen sag curve
The deoxygenation caused by microbial decompostion of
waste and oxygenation by reaeration
Rate of deoxygenation =
 kd = the deoxygenation rate constant (per day)
Lt = the BOD remaining t(days) after the wastes enter the river
So , rate of deoxygenation = ---------(1)

8.  Rate of Reaeration =
 kr = reaeration constant (per time)
 D = dissolved oxygen deficit
(D = DOs – DO)
DOs = saturated value of dissolved oxygen ,
DO = actual dissolved oxygen .
From (1) &(2) : -
Rate of increase of the deficit =rate of deoxygenation – rate of
reaeration
------------(2)
-------- -- (3)

9.  Which has solution :
we can write the equation for the DO as :-
from equ. (4) :-
 Equation (5) is classic streeter phelps oxygen sag model first described in
1925.
 When :- kr = kd
from equ. -------(4)
D = (kdL0t + D0)e-kdt ----------(6)
If the stream has a constant cross sectional area &traveling u , then time &
distance downstream related by
----------(4)
----------(5)

10. x = ut
where
x = distance downstream
u = stream speed
t = time
From equ. (4)
----------(7)

11. The Streeter-Phelps equation:
D = dissolved oxygen deficit (DO saturation minus the
actual level of DO) (mg /L)
D0 = dissolved oxygen deficit at x = 0 (mg /L)
ka = first-order reaeration rate coefficient (d-1)
x = distance (m)
u = average velocity (m /s)
kd = first-order deoxygenation rate constant (d-1)
L0 = CBOD (mg /L)

13. CONT…

15. MECHANISM
The model is based on the assumption that
dissolved oxygen concentration is dependent on
two independent processes: decomposition of
organic matter and reaeration.
 Both processes are described as first order
reactions . The model is based on plug flow
hydraulics.

16. CONT……………
When the oxygen
demand is less than
the reaeration rate,
the concentration of
DO increases until it
reaches atmospheric
eqilibrium.
When the oxygen
demand is greater
than the reaeration
rate,concentration of
DO decrease.

17. Limitations of the DO Sag Equation
 Steady state -- Streams aren't steady state. Flows, velocities, geometries,
and temperatures all vary with time.
 Plug flow -- Streams aren't really plug flow.
 Algae -- The model doesn't include algae which are a very important source of
oxygen
 Benthic organisms -- The model assumes that all the oxygen demand is from
suspended organisms