A bottle with a volume of 190 U. S. fluid gallons is filled at the rate of 1.8 g/min. (Water has a density of 1000 kg/m3, and 1 U.S. fluid gallon = 231 in.3.) In years, how long does the filling take?
1 US fl.gal
=231 in³
=231*(2.54³) cm³
=231*(2.54³) g (weight)
Time required to fill "bottle"
=190 US fl.gal / 1.8 g/min
=190*(231*(2.54³))/1.8 min.
Convert result to year(s).
To find out how long it takes to fill the bottle, we need to calculate the total volume of water that needs to be filled and then divide it by the filling rate.
First, let's convert the given volume of the bottle from U.S. fluid gallons to cubic meters (m^3) using the conversion factor given: 1 U.S. fluid gallon = 231 in^3.
So, the volume of the bottle in cubic meters is:
190 U.S. fluid gallons * (231 in^3 / 1 U.S. fluid gallon) * (1 m^3 / (39.37 in)^3) = 0.3338 m^3 (approximately).
We also need to convert the filling rate from grams per minute (g/min) to cubic meters per minute (m^3/min). To do this, we need to consider the density of water, which is given as 1000 kg/m^3.
The mass of water that fills the bottle in grams per minute is the same as the volume in cubic meters (since the density of water is 1000 kg/m^3).
So, the filling rate in cubic meters per minute is:
1.8 g/min * (1 kg/1000 g) * (1 m^3 / 1000 kg) = 0.0018 m^3/min (approximately).
Now we can find the time it takes to fill the bottle by dividing the volume of the bottle by the filling rate:
Time = Volume / Filling rate = 0.3338 m^3 / 0.0018 m^3/min = 185.4 minutes (approximately).
To convert this time to years, we need to know the number of minutes in a year. There are 60 minutes in an hour, 24 hours in a day, and approximately 365.25 days in a year.
So, the conversion factor from minutes to years is:
1 year = 365.25 days/year * 24 hours/day * 60 minutes/hour = 525,960 minutes (approximately).
Finally, we can calculate the time in years by dividing the time in minutes by the conversion factor:
Time in years = 185.4 minutes / 525,960 minutes/year = 0.000352 (approximately).
Therefore, it takes approximately 0.000352 years to fill the bottle.
To find the time it takes to fill the bottle, we need to convert its volume from gallons to cubic meters.
Given:
Volume of the bottle = 190 U.S. fluid gallons
Density of water = 1000 kg/m^3
1 U.S. fluid gallon = 231 in^3
First, we convert gallons to cubic inches:
190 U.S. fluid gallons * 231 in^3/gallon = 43,890 in^3
Next, we convert cubic inches to cubic meters:
43,890 in^3 * (0.0254 m / 1 in)^3 = 0.719 m^3
Now, we can calculate the time it takes to fill the bottle:
Volume of water = 0.719 m^3
Flow rate = 1.8 g/min
Since the density of water is 1000 kg/m^3, we can calculate the mass of water:
Mass = Density * Volume
Mass = 1000 kg/m^3 * 0.719 m^3 = 719 kg
Now, we can calculate the time it takes to fill the bottle:
Time = Mass / Flow rate
Time = 719 kg / (1.8 g/min * (1 kg / 1000 g) * (60 min / 1 hour))
Time = 719 kg / (1.8 * 10^-3 kg/min)
Time = 719,000 min
Since there are 60 minutes in an hour and 24 hours in a day, we can convert minutes to years:
Time = 719,000 min * (1 hour / 60 min) * (1 day / 24 hours) * (1 year / 365 days)
Time = 8.2 years (approximately)
Therefore, it takes approximately 8.2 years to fill the bottle.