An average family of four uses roughly 1600 liters (about 400 gallons) of water per day. (One liter = 1000 cm3.) How much depth would a lake lose per year if it uniformly covered an area of 90 square kilometers and supplied a local town with a population of 30000 people? Consider only population uses, and neglect evaporation and so on.
5566
To find out how much depth a lake would lose per year, we need to calculate the total volume of water used by the local town in a year.
Step 1: Calculate the total water used by the local town per day.
An average family of four uses 1600 liters of water per day.
Number of families in the local town = Number of people in the town / Average family size
Number of families = 30000 / 4 = 7500 families
Total water used per day by the local town = Water used per family * Number of families
Total water used per day = 1600 liters * 7500 families = 12,000,000 liters
Step 2: Convert liters to cubic centimeters.
1 liter = 1000 cubic centimeters (cm³)
Total water used per day in cm³ = Total water used per day * 1000
Total water used per day in cm³ = 12,000,000 liters * 1000 = 12,000,000,000 cm³
Step 3: Calculate the total water used per year.
Since we know that there are 365 days in a year, we can calculate the total water usage per year.
Total water used per year = Total water used per day in cm³ * 365 days
Total water used per year = 12,000,000,000 cm³ * 365 days = 4,380,000,000,000 cm³
Step 4: Calculate the depth lost by the lake.
To calculate the depth lost by the lake, we need to know the initial volume of water in the lake.
Volume of water = Area of the lake * Depth of the lake
Area of the lake = 90 square kilometers = 90,000,000 square meters
Since the lake is assumed to have uniform depth,
Volume of water in the lake = Area of the lake * Initial depth
Now, let's calculate the depth lost per year. From the given information, lets assume there is an initial depth of 1 meter.
Initial volume of water = 90,000,000 square meters * 1 meter = 90,000,000 cubic meters
Volume lost per year = Total water used per year in cm³ / 1000000 (to convert from cm³ to cubic meters)
Volume lost per year = 4,380,000,000,000 cm³ / 1,000,000 = 4,380,000 cubic meters
Since the volume of water lost per year is the same as the volume lost in depth, we can calculate the depth lost by dividing the volume lost per year by the area of the lake.
Depth lost per year = Volume lost per year / Area of the lake
Depth lost per year = 4,380,000 cubic meters / 90,000,000 square meters ≈ 0.0486667 meters
Therefore, the lake would lose approximately 0.0486667 meters or 4.86667 centimeters of depth per year due to the water usage of the local town.