An industry discharges 0.8 m³/s of a waste with a 5-day CBOD of 600 mg/L to a river with a flow of 4 m³/s and a 5-day CBOD of 8 mg/L. Calculate the 5-day CBOD of the river after mixing with the waste.
An industry discharges 0.8 m³/s of a waste with a 5-day CBOD of 600 mg/L to a river with a flow of 4 m³/s and a 5-day CBOD of 8 mg/L. Calculate the 5-day CBOD of the river after mixing with the waste.
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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![### Problem Statement
An industry discharges 0.8 m³/s of a waste with a 5-day CBOD of 600 mg/L to a river with a flow of 4 m³/s and a 5-day CBOD of 8 mg/L. Calculate the 5-day CBOD of the river after mixing with the waste.
### Explanation
This problem involves calculating the 5-day Carbonaceous Biochemical Oxygen Demand (CBOD) of a river after it receives discharge from an industry. To solve this, you can use the principle of conservation of mass for CBOD concentrations:
#### Formula:
The mixed CBOD concentration (\( C_m \)) can be calculated using the formula:
\[
C_m = \frac{Q_w \times C_w + Q_r \times C_r}{Q_w + Q_r}
\]
Where:
- \( Q_w \) = discharge flow rate of waste (0.8 m³/s)
- \( C_w \) = CBOD concentration of waste (600 mg/L)
- \( Q_r \) = flow rate of the river (4 m³/s)
- \( C_r \) = CBOD concentration of the river (8 mg/L)
#### Calculation Steps:
1. **Determine Total Flow:**
\[
Q_{\text{total}} = Q_w + Q_r = 0.8 + 4.0 = 4.8 \text{ m}^3/\text{s}
\]
2. **Calculate Mixed CBOD:**
\[
C_m = \frac{(0.8 \times 600) + (4.0 \times 8)}{4.8} = \frac{480 + 32}{4.8}
\]
3. **Simplify:**
\[
C_m = \frac{512}{4.8} \approx 106.67 \text{ mg/L}
\]
#### Result
The 5-day CBOD of the river after mixing with the industrial discharge is approximately **106.67 mg/L**.
This calculation is crucial for understanding the environmental impact of industrial waste on river ecosystems and ensuring compliance with environmental regulations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F093e7116-3e01-49ad-9157-7a22a5caeb16%2F476bebce-e980-4194-8caa-a1e7a1eb5457%2Fx7kepjj_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
An industry discharges 0.8 m³/s of a waste with a 5-day CBOD of 600 mg/L to a river with a flow of 4 m³/s and a 5-day CBOD of 8 mg/L. Calculate the 5-day CBOD of the river after mixing with the waste.
### Explanation
This problem involves calculating the 5-day Carbonaceous Biochemical Oxygen Demand (CBOD) of a river after it receives discharge from an industry. To solve this, you can use the principle of conservation of mass for CBOD concentrations:
#### Formula:
The mixed CBOD concentration (\( C_m \)) can be calculated using the formula:
\[
C_m = \frac{Q_w \times C_w + Q_r \times C_r}{Q_w + Q_r}
\]
Where:
- \( Q_w \) = discharge flow rate of waste (0.8 m³/s)
- \( C_w \) = CBOD concentration of waste (600 mg/L)
- \( Q_r \) = flow rate of the river (4 m³/s)
- \( C_r \) = CBOD concentration of the river (8 mg/L)
#### Calculation Steps:
1. **Determine Total Flow:**
\[
Q_{\text{total}} = Q_w + Q_r = 0.8 + 4.0 = 4.8 \text{ m}^3/\text{s}
\]
2. **Calculate Mixed CBOD:**
\[
C_m = \frac{(0.8 \times 600) + (4.0 \times 8)}{4.8} = \frac{480 + 32}{4.8}
\]
3. **Simplify:**
\[
C_m = \frac{512}{4.8} \approx 106.67 \text{ mg/L}
\]
#### Result
The 5-day CBOD of the river after mixing with the industrial discharge is approximately **106.67 mg/L**.
This calculation is crucial for understanding the environmental impact of industrial waste on river ecosystems and ensuring compliance with environmental regulations.
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