DO SAG CURVE-

CHAPTER 1WATER QUALITY PARAMETERS

Streeter-Phelps oxygen sag equation

DO drops rapidly

dissolved oxygen

reaches its minimum value

and river conditions are at

their worst

Beyond the critical

point, the remaining organic

matter in the river has diminished

to the point where oxygen is

being added to the river by

reaeration faster than it is being

withdrawn by decomposition, and

the river begins to recover.

A city discharges 20000 m3/day of sewage into a river whose

rate of flow is 0.7 m3/sec. Determine critical DO & time and

DO deficit profile for 100 km from the following data:

Given: Velocity of mix = 0.25 m/s, kr=0.4/day, kd = 0.23/day

Calculate Critical time (tc) and DO (Dc)

Ultimate mixed BOD

Initial DO deficit = DOs - DOmix

Solution

Q River = 0.7 m3/sec

Q Sewage discharge = 20000/(24x 3600) = 0.231 m3/sec

MASS BALANCE

𝐶 =𝑄𝑢𝐶𝑢 + 𝑄𝑑𝐶𝑑𝑄𝑢 + 𝑄𝑑

BOD of mix

𝐵𝑂𝐷 =(0.7)(3.4) + (0.231)(45)

0.7 + 0.231= 13.71 mg/l

DO of mix

𝐷𝑂 =(0.7)(8.2) + (0.231)(0.2)

0.7 + 0.231= 6.66 mg/l

Temperature of mix

𝑇 =(0.7)(23) + (0.231)(26)

0.7 + 0.231= 23.74 oC

Saturation value of D.O. at 23.74 oC is 8.57 mg/l

Ultimate BOD 𝐵𝑂𝐷𝑡 = 𝐵𝑂𝐷𝑢 (1 − 𝑒−𝑘𝑡)

13.71 = 𝐵𝑂𝐷𝑢 (1 − 𝑒−0.23(5))

𝐵𝑂𝐷𝑢 = 𝐿𝑜 = 20.88 𝑚𝑔/𝐿

Initial DO deficit (D0)

𝐷𝑜 = 8.57 − 6.66 = 1.91 𝑚𝑔/𝐿

Adjustments to

Deoxygenation (kd) and reoxygenation (kr) coefficients at 23.74 oC temperature

𝑘𝑑 = 0.23 × 1.056(23.74−20) = 0.282 𝑘𝑟 = 0.4 × 1.024(23.74−20) = 0.437

Solve tc & Dc

DO deficit at 20, 40, 80 & 100 km??