Question

The wastewater has a DO concentration of 4 mg/L when it is discharged. The river, just upstream of the outfall, has a DO concentration of 8 mg/L.The temperatures of the sewage and river are 15 oC; at this temperature the saturated DO concentration is 10.08 mg/L. What is the initial oxygen deficit of the mixture, just downstream of the discharge point

Answer 1

the initial deficit of oxygen of the mixture just downstream of the discharge point = 2.44 mg/L

Step-by-step explanation:

From the diagram ; we determine the dissolved oxygen just downstream by using the equation

`DO = (Q_wL_w+Q_rL_r)/(Q_w+Q_r)`

where;

`Q_w` = volumetric flow rate of waste water = 1 m³/s

`Q _r` = volumetric flow rate of river just upstream of discharge point = 10 m³/s

`L_w` = ultimate BOD of waste water = 4 mg/L

`L_r` = ultimate BOD of mixture of the stream water and waste water = 8 mg/L

∴ DO =
`((1 \ m^3/s)(4 \ mg/L ) + ( 10 \ m^3/s) ( 8 \ mg/L))/((1 \ m^3/s)+(10 \ m^3 / s))`

DO = 7.64 mg/L

Now; to calculate the initial deficit of oxygen; we use the formuale

`D_0 = DO _(sat) - DO`

where;

`DO_(sat)` = the saturated value of the dissolved oxygen

since no presence of chloride in the stream; chloride concentration = 0 mg/L

However, we obtain the saturated dissolved oxygen from Table - 5.10 " Solubility of oxygen in water at 1 atm corresponding to the temperature at 15° C and 0 mg/L concentration of chloride = 10.08 mg/L

SO,

`D_0 = DO _(sat) - DO`

`D_0 = 10.08 \ mg/L - 7.64 \ mg/L`

`D_0 = 2.44 \ mg/L`

Thus; the initial deficit of oxygen of the mixture just downstream of the discharge point = 2.44 mg/L