An average family of four uses roughly 1200 liters (300 gallons) of water per day. (One liter = 1000 cm^3.) How much depth would a lake lose per year if it uniformly covered an area of 50 square kilometers and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation and so on.
Assume 40,000 people use the same amount as 10,000 families of 4. The total water use per day will be 1200*10^4 = 1.2*10^7 liters = 1.2*10^4 m^3. Per year that is V = 4.38*10^6 m^3.
The drop in water level per year is V/A, where A is the area of the lake, 50*10^6 m^3.
So, would that make it 8.76*10^-2? If so, what would the units be?
Yes, in meters. That's about 3 1/2 inches
To calculate the depth a lake would lose per year, we need to determine the total volume of water used by the local town in one year.
First, let's calculate the water usage per person per day:
Water usage per person = 1200 liters / 4 people
Water usage per person = 300 liters per person
Next, we'll calculate the total water usage per day by the population:
Total water usage per day = Water usage per person * Population
Total water usage per day = 300 liters/person * 40,000 people
Now let's convert the liters to cubic centimeters (cm^3):
Total water usage per day = 300 liters/person * 40,000 people * 1000 cm^3/liter
To calculate the total volume of water used per year, we multiply the total water usage per day by 365 (days in a year):
Total water usage per year = Total water usage per day * 365
Next, we'll calculate the area of the lake in square centimeters:
Area of the lake = 50 square kilometers * 1,000,000 square meters/kilometer * 10,000 square centimeters/square meter
Finally, to determine the depth the lake would lose per year, we divide the total water usage by the lake area:
Depth loss per year = Total water usage per year / Area of the lake
Let's perform the calculations step-by-step:
Water usage per day = 300 liters/person * 40,000 people * 1000 cm^3/liter
Total water usage per day = 1.2 × 10^10 cm^3
Total water usage per year = Total water usage per day * 365
Total water usage per year = 1.2 × 10^10 cm^3 * 365
Total water usage per year = 4.38 × 10^12 cm^3
Area of the lake = 50 square kilometers * 1,000,000 square meters/kilometer * 10,000 square centimeters/square meter
Area of the lake = 5 × 10^12 cm^2
Depth loss per year = Total water usage per year / Area of the lake
Depth loss per year = 4.38 × 10^12 cm^3 / 5 × 10^12 cm^2
Depth loss per year = 0.876 cm
Therefore, the lake would lose approximately 0.876 centimeters of depth per year due to the water usage by the local town.