Calculate Fill Rate for 183 US Gallon Bottle

[AnkhUNC]

Homework Statement

A bottle with a volume of 183 U. S. fluid gallons is filled at the rate of 1.7 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?

Homework Equations

The Attempt at a Solution

Volume -> 42273 Units in.^3 -> 692730.3565 Units cm^3 -> .6927303565 Units m^3

But after this finding the mass of water and the fill rate I get messed up. I know is just simple conversion but I'm messing something up down the line.

 

[blochwave]

Well first, I can't really follow your work and only have trusty windows calculator if I wanted to, so I'll just say...

Actually yes I can, I see, you figured out how many cubic meters 183 gallons is, right?

mmk

If water has a density of 1000 kg/m^3, that's saying a m^3 of water has a mass of 1000 kg. You want to find out how much mass is in .6927 m^3. Can you do that? That's just a simple conversion or ratio or whatever you want to call it. So you need x g of water(you find x)

Then you know you have 1.7g/min, so convert that to xg/zyears, and you're looking for z, if there's 1.7 grams every minute, how many years are there for every x grams?

Here's a fun thing google calculator does
http://www.google.com/search?hl=en&rls=com.microsoft:en-US&q=183+gallons+to+m^3

but remember you won't have it on a test, so just use it to check your answers confidently

 

[Moetasim]

To calculate the fill rate for the 183 US gallon bottle, we first need to convert the volume from gallons to cubic meters. Using the conversion factor of 1 US fluid gallon = 231 cubic inches, we can convert 183 gallons to 42273 cubic inches. Then, we can convert cubic inches to cubic meters by dividing by 61023.7 (1 cubic meter = 61023.7 cubic inches). This gives us a volume of approximately 0.6927 cubic meters.

Next, we need to calculate the mass of water in the bottle. Using the given density of water (1000 kg/m^3), we can multiply the volume by the density to get a mass of approximately 692.7 kg.

Now, we can use the given fill rate of 1.7 g/min to calculate the time it takes to fill the bottle. First, we need to convert the fill rate from grams to kilograms by dividing by 1000 (1 kg = 1000 g). This gives us a fill rate of 0.0017 kg/min. Then, we can divide the mass of water (692.7 kg) by the fill rate (0.0017 kg/min) to get the time it takes to fill the bottle. This gives us approximately 407,470 minutes, or approximately 283 days.

In summary, it would take approximately 283 days to fill a 183 US gallon bottle with a fill rate of 1.7 g/min.