Answer :
To determine the volume of the discrete (grab) sample to be collected at 1800 for a 500 milliliter composite sample for COD analysis, we need to follow these steps:
1. Identify the Flow Rates at Each Time Interval:
- 0000/2400 hours: 1 million gallons per day (MGD)
- 0600 hours: 5 MGD
- 1200 hours: 4 MGD
- 1800 hours: 2 MGD
2. Calculate the Total Flow Over the Day:
- Sum the flow rates at each time interval:
[tex]\[ 1 \text{ MGD} + 5 \text{ MGD} + 4 \text{ MGD} + 2 \text{ MGD} \][/tex]
[tex]\[ = 12 \text{ MGD} \][/tex]
3. Understand the Total Composite Sample Volume:
- We are given that the total composite sample volume to be created is 500 milliliters.
4. Determine the Proportion of Flow at 1800 Hours Relative to the Total Flow:
- The flow rate at 1800 hours is 2 MGD.
- The total flow over the day is 12 MGD.
5. Calculate the Volume of the Grab Sample to be Collected at 1800:
- The volume of the grab sample to be collected is proportional to the flow rate at 1800 hours. To find this, use the fractional share of the 1800 flow relative to the total flow and multiply by the total composite volume:
[tex]\[ \text{Grab Sample Volume} = \left(\frac{\text{Flow at 1800}}{\text{Total Flow}}\right) \times \text{Total Composite Volume} \][/tex]
[tex]\[ = \left(\frac{2 \text{ MGD}}{12 \text{ MGD}}\right) \times 500 \text{ milliliters} \][/tex]
[tex]\[ = \left(\frac{2}{12}\right) \times 500 \text{ milliliters} \][/tex]
[tex]\[ = \left(\frac{1}{6}\right) \times 500 \text{ milliliters} \][/tex]
[tex]\[ = 83.33 \text{ milliliters} \][/tex]
So, the volume of the discrete (grab) sample to be collected at 1800 is 83.33 milliliters.
1. Identify the Flow Rates at Each Time Interval:
- 0000/2400 hours: 1 million gallons per day (MGD)
- 0600 hours: 5 MGD
- 1200 hours: 4 MGD
- 1800 hours: 2 MGD
2. Calculate the Total Flow Over the Day:
- Sum the flow rates at each time interval:
[tex]\[ 1 \text{ MGD} + 5 \text{ MGD} + 4 \text{ MGD} + 2 \text{ MGD} \][/tex]
[tex]\[ = 12 \text{ MGD} \][/tex]
3. Understand the Total Composite Sample Volume:
- We are given that the total composite sample volume to be created is 500 milliliters.
4. Determine the Proportion of Flow at 1800 Hours Relative to the Total Flow:
- The flow rate at 1800 hours is 2 MGD.
- The total flow over the day is 12 MGD.
5. Calculate the Volume of the Grab Sample to be Collected at 1800:
- The volume of the grab sample to be collected is proportional to the flow rate at 1800 hours. To find this, use the fractional share of the 1800 flow relative to the total flow and multiply by the total composite volume:
[tex]\[ \text{Grab Sample Volume} = \left(\frac{\text{Flow at 1800}}{\text{Total Flow}}\right) \times \text{Total Composite Volume} \][/tex]
[tex]\[ = \left(\frac{2 \text{ MGD}}{12 \text{ MGD}}\right) \times 500 \text{ milliliters} \][/tex]
[tex]\[ = \left(\frac{2}{12}\right) \times 500 \text{ milliliters} \][/tex]
[tex]\[ = \left(\frac{1}{6}\right) \times 500 \text{ milliliters} \][/tex]
[tex]\[ = 83.33 \text{ milliliters} \][/tex]
So, the volume of the discrete (grab) sample to be collected at 1800 is 83.33 milliliters.
