A development in a town was designed to accomodate 10,000 people, in 2,000, 5 units building, each person in this settlement uses an average of 5 gallons of water per day for washing purposes. As an engineering technician you are required to design a waste water treatment clarifier tank, rectangular in shape. Detention time using this clarifier should be 3.5 hours, with an overflow rate of 30 gallons per day. What should the dimensions of this clarifier tank be?

Note 1 US gallon = 0.0037854 m3

To design the waste water treatment clarifier tank, we need to determine its dimensions based on the given information.

Step 1: Calculate the total wastewater flow rate
The total wastewater flow rate can be calculated by multiplying the number of people in the settlement by the average water usage per person per day.
Total wastewater flow rate = 10,000 people × 5 gallons/person/day

Step 2: Convert the total wastewater flow rate to cubic meters (m^3)
Since 1 US gallon is equal to 0.0037854 m^3, we need to convert the total wastewater flow rate to cubic meters.
Total wastewater flow rate in m^3/day = Total wastewater flow rate in gallons/day × 0.0037854 m^3/gallon

Step 3: Calculate the flow rate required for detention time and overflow rate
The flow rate required for detention time can be calculated by dividing the total wastewater flow rate by the detention time.
Flow rate for detention time = Total wastewater flow rate in m^3/day ÷ Detention time

The flow rate required for overflow rate is given as 30 gallons/day. We need to convert it to cubic meters.
Flow rate for overflow rate = 30 gallons/day × 0.0037854 m^3/gallon

Step 4: Calculate the dimensions of the clarifier tank
To calculate the dimensions of the clarifier tank, we can use the flow rate for detention time. The dimensions of a rectangular tank can be calculated by dividing the flow rate by the overflow rate and multiplying it by the width and depth of the clarifier tank.
Width × Depth × Flow rate for detention time = Flow rate for overflow rate

Now, you can substitute the values and solve for the dimensions of the clarifier tank. Make sure to use consistent units throughout the calculations.