an average family of four uses roughly 1200 liters (about 300 gallons) of water per day (1 liter=1ooocm cubed) . how much depth would a lake lose per uear if it uniformly covered an area of 50 square kilometers and supplied a llocal town with a population of 40,000 people ----
this is from a textbook, but I do know which one it is
Calculate the volume used per year, V, in cubic metres. Note that there are 1000 l. in 1 m³.
Calculate the surface area of the lake in square metres, A.
The decrease in depth, D, is V/A metres, assuming no river feeds the lake, and no change in volume due to evaporation and rain.
V=1200 (l.)/1000 (l/m³)*40000 (people) * 365 (days)
=1200/1000*40000*365 m³
S=50 (km²)=50*1000*1000 (m²)
Calculate V, S and D=V/S
50,000,000 sq m
1.2x10,000 (10,000 families of 4 = 40,000 people)
12,000 m^3 per day * 365 days = 4,380,000 m ^3 per year
Depth = 4,380,000 m ^3 / 50,000,000
Depth lost = 0.0876 m^3
To calculate the depth a lake would lose per year, we need to find the total volume of water consumed by the town and divide it by the surface area of the lake.
Step 1: Calculate the total water consumed by the town per day.
An average family of four uses 1200 liters of water per day.
So, the total water consumed by the town per day is:
1200 liters/family * 4 families = 4800 liters/day
Step 2: Calculate the total water consumed by the town per year.
Assuming there are 365 days in a year, the total water consumed by the town per year is:
4800 liters/day * 365 days = 1,752,000 liters/year
Step 3: Convert liters to cubic centimeters.
1 liter = 1000 cubic centimeters, so the total water consumed by the town per year is:
1,752,000 liters/year * 1000 cm^3/liter = 1,752,000,000 cm^3/year
Step 4: Calculate the volume of the lake.
The lake uniformly covers an area of 50 square kilometers. Since we know that 1 km^2 = 1,000,000 m^2, the area of the lake in square meters is:
50 km^2 * 1,000,000 m^2/km^2 = 50,000,000 m^2
Step 5: Calculate the depth the lake would lose per year.
The volume of the lake is equal to the surface area multiplied by the average depth. Hence, we can calculate the average depth:
Average Depth = Volume / Area
Average Depth = 1,752,000,000 cm^3/year / 50,000,000 m^2
Now, we need to convert cm^3 to meters cubed:
1 cm^3 = 0.000001 m^3
So, the average depth is:
Average Depth = (1,752,000,000 cm^3/year * 0.000001 m^3/cm^3) / 50,000,000 m^2
Simplifying the equation gives us:
Average Depth = 0.03504 meters
Therefore, the lake would lose approximately 0.03504 meters (or 3.504 centimeters) of depth per year.
To solve this problem, we first need to determine the total amount of water used by the local town in a year, and then calculate the depth the lake would lose.
Step 1: Calculate the town's water usage per year:
The average family of four uses 1200 liters of water per day.
So, the total water usage for the town can be calculated as follows:
Water used per day = (1200 liters/family) * (number of families) = (1200 liters/family) * (number of families in the town)
Number of families in the town = number of people in the town / number of people in a family
Number of people in a family = 4 (given)
Number of people in the town = 40,000 (given)
Number of families in the town = 40,000 / 4 = 10,000
Water used per year = water used per day * 365 days/year
Water used per year = (1200 liters/family) * (10,000 families) * 365 days/year
Step 2: Convert the water usage to cubic meters:
1 liter = 1000 cm³ = 0.001 m³
Water used per year (in cubic meters) = (water used per year in liters) * (0.001 m³/liter)
Step 3: Calculate the lake's surface area:
The lake uniformly covers an area of 50 square kilometers.
Since 1 square kilometer = 1,000,000 m²,
Lake's surface area = 50 * 1,000,000 m²
Step 4: Calculate the depth the lake would lose:
The change in depth of the lake is determined by dividing the water volume used by the area it covers.
Change in depth = (Water used per year in cubic meters) / (Lake's surface area)
Now, you can substitute the values into the equations to calculate the result.