## Problem Restatement**Design a septic tank to treat wastewater from an institute with:** - Number of users = 50 persons - Water consumption = 100 liters per capita per day (lpcd) - Desludging period = 2 years --- ## Step-by-Step Solution ### **Step 1: Calculate Total Wastewater Generated per Day** \[ \text{Total wastewater/day} = \text{Number of users} \times \text{Water consumption} \] \[ = 50 \times 100 = 500 \text{ liters/day} \] --- ### **Step 2: Determine Retention Time** **Standard retention time for septic tank:** - Domestic sewage: **24 hours** (1 day) --- ### **Step 3: Calculate Volume Required for Liquid** \[ \text{Volume for liquid} = \text{Total wastewater/day} \times \text{Retention time} \] \[ = 500 \text{ liters} \times 1 \text{ day} = 500 \text{ liters} \] \[ = 5. \text{ m}^3 \qquad (1 \text{ m}^3 = 100 \text{ liters}) \] --- ### **Step 4: Calculate Sludge and Scum Accumulation** #### **A. Sludge Accumulation** - **Sludge production:** 30 liters/person/year (standard value) - Over 2 years: \[ \text{Total sludge} = 50 \times 30 \times 2 = 300 \text{ liters} \] \[ = 3. \text{ m}^3 \] #### **B. Scum Accumulation** - **Scum production:** 30 liters/person/year (approximate, similar to sludge) \[ \text{Total scum} = 50 \times 30 \times 2 = 300 \text{ liters} \] \[ = 3. \text{ m}^3 \] --- ### **Step 5: Calculate Total Tank Volume** \[ \text{Total volume required} = \text{Volume for liquid} + \text{Sludge} + \text{Scum} \] \[ = 5. + 3. + 3. = 11. \text{ m}^3 \] **Add 10% freeboard (for safety):** \[ \text{Freeboard} = .10 \times 11. = 1.1 \text{ m}^3 \] \[ \text{Total volume} = 11. + 1.1 = 12.1 \text{ m}^3 \] --- ### **Step 6: Propose Septic Tank Dimensions** A typical proportion for septic tanks is: **Length : Width : Depth = 3 : 1 : 1.5** Let width = \( w \) Length = \( 3w \) Depth = \( 1.5w \) \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Depth} \] \[ 12.1 = 3w \times w \times 1.5w = 4.5w^3 \] \[ w^3 = \frac{12.1}{4.5} = 2.689 \] \[ w = \sqrt[3]{2.689} \approx 1.39 \text{ m} \] So, - **Width** = 1.39 m - **Length** = 3 × 1.39 = **4.17 m** - **Depth** = 1.5 × 1.39 = **2.09 m** --- ## **Final Answer** ### **Septic Tank Design Summary** - **Capacity:** **12.1 m³** - **Dimensions (approx.):** - **Length:** 4.2 m - **Width:** 1.4 m - **Depth:** 2.1 m - **Retention Time:** 24 hours - **Desludging Period:** 2 years --- ### **Notes** - Adjust dimensions as per site conditions. - Provide inlet and outlet chambers, baffle walls, and manhole covers as per standard practice.