An average family of four uses roughly 1200 liters (about 3600 gallons) of water per day. (One liter = 1000cm3.) 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 60,000 people?
To find out how much depth a lake would lose per year, we need to calculate the total volume of water used by the town and then divide it by the surface area of the lake.
Step 1: Calculate the daily water usage of the town.
The average family of four uses 1200 liters of water per day. So, the total water usage by the town can be calculated by multiplying the average water usage per family by the number of families in the town.
Water usage per day = 1200 liters/family × (60,000 people / 4 people per family)
Water usage per day = 1200 liters/family × 15,000 families
Step 2: Convert liters to cubic centimeters (cm³).
Since 1 liter is equal to 1000 cm³, we need to convert liters to cm³.
Water usage per day = 1200 liters/family × 15,000 families × 1000 cm³/liter
Step 3: Calculate the annual water usage of the town.
To find the annual water usage, we multiply the water usage per day by the number of days in a year.
Annual water usage = Water usage per day × 365 days
Step 4: Calculate the depth loss of the lake.
To find the depth lost by the lake, divide the annual water usage by the surface area of the lake.
Depth loss = Annual water usage / Surface area of the lake
Now, let's plug in the values and calculate the depth loss of the lake:
Surface area of the lake = 50 km² = 50,000,000 m²
Water usage per day = 1200 liters/family × 15,000 families × 1000 cm³/liter = 18,000,000,000 cm³
Annual water usage = Water usage per day × 365 days = 18,000,000,000 cm³ × 365 = 6,570,000,000,000 cm³
Depth loss = Annual water usage / Surface area of the lake = 6,570,000,000,000 cm³ / 50,000,000 m² = 131.4 cm
Therefore, the lake would lose approximately 131.4 centimeters (or 1.31 meters) of depth per year if it uniformly covered an area of 50 square kilometers and supplied a local town with a population of 60,000 people.