Question

A river is having discharge of 22 m³/s receives wastewater discharge of 0.5 m³/s. The initial DO of the river water is 6.3 mg/L, and DO content in the wastewater is 0.6 mg/L. The five day BOD in the river water is 3 mg/L, and the wastewater added to river has five day BOD of 130 mg/L. Consider saturation DO of 8.22 mg/L and deoxygenation and reoygenation constant values of 0.1 and 0.3 per day, respectively. Find critical DO deficit and DO in the river after one day?. The average velocity of flow in the stream after mixing of wastewater is 0.18 m/sec.​

Answer 1

Critical DO deficit: 2.91 mg/L

DO in the river after one day: 5.62 mg/L

Step-by-step explanation:

We can use the Streeter-Phelps equation, which is a mathematical model that describes how dissolved oxygen (DO) decreases in a river or stream along a certain distance by degradation of biochemical oxygen demand (BOD).

Step 1: Calculate the average BOD concentration in the river after mixing of wastewater

BOD_avg = (Q_r * BOD_r + Q_w * BOD_w) / (Q_r + Q_w)

BOD_avg = (22 m³/s * 3 mg/L + 0.5 m³/s * 130 mg/L) / (22 m³/s + 0.5 m³/s)

BOD_avg = 11.3 mg/L

Step 2: Calculate the critical DO deficit

D_c = (K_d * BOD_avg) / (K_r - K_d)

D_c = (0.1 per day * 11.3 mg/L) / (0.3 per day - 0.1 per day)

D_c = 2.91 mg/L

Step 3: Calculate the DO in the river after one day

DO_1 = DO_r - K_d * (DO_r - S_DO) - K_r * D_c

DO_1 = 6.3 mg/L - 0.1 per day * (6.3 mg/L - 8.22 mg/L) - 0.3 per day * 2.91 mg/L

DO_1 = 5.62 mg/L