Questions and answers on how to convert things from one unit or system to another



Postby guest » Wed Sep 08, 2004 11:07 pm

I need to convert 1000 kg/m^3 to LBM/Ft^3. My engineering notes make no sense

Re: help

Postby Knight » Thu Sep 09, 2004 10:12 pm

guest wrote:I need to convert 1000 kg/m^3 to LBM/Ft^3. My engineering notes make no sense

Again, the answer to this is the old conversion standby, Unit Analysis.

You have in the problem you've given, you need to convert 1000 kg to pounds, and cubic meters to cubic feet.

So we need to know how many pounds there are in a kilogram, and how many cubic feet there are in a cubic meter.

You can look both of these up using the conversion tables here, and find that there are 2.205 lbs per kg, and there are 35.31 cubic feet per cubic meter.

To talk though this, we can multiply 1000 kg/m³ by 2.205 lbm/kg, giving us 2,205 lbm/m³. Next, convert m³ to ft³ by multiplying the numerator (1 kg) by 35.31, giving us 2,205 lbm/35.31 ft³. Now divide this out: 2205 lbm/35.31 ft³ = 62.45 lbm/ft³.

I've found that the best way to do the exersize that I went through above is to use something called the "railroad tracks." Start by putting the initial value you have on paper:
Code: Select all
1000 kg |
     m³ |

Now, in this problem, we need to convert kg to lbm. As you recall, thats 2.205 lbm/kg. So put that down.
Code: Select all
1000 kg | 2.205 lbm |
     m³ |        kg |

Now, you'll notice that you've got kg in the top, and kg on the bottom... That means you can cancel them out, leaving you with lbm/m³! But lets not do that just yet. Lets get convert m³ to ft³ as well. We'll want to have m³ in the numerator, and ft³ in the denominator in order for it to cancel, so:
Code: Select all
1000 kg | 2.205 lbm |     1 m³  |
     m³ |        kg | 35.31 ft³ |

Now, lets do the cancelling: kg's cancel out, and m³'s cancel out, leaving us with:
Code: Select all
1000    | 2.205 lbm |     1     |
        |           | 35.31 ft³ |

Now, simplify the equation: 1000 · 2.205 lbm · 1 / 35.31 ft³ = 62.45 lbm/ft³.

The wonderful thing about this type of unit analysis is that you can convert to any equivilant units. For example, there's no need to remember that there are 3.15Ee7 seconds per year; you can use units you remember to derive it: Years to days, days to hours, hours to minutes, minutes to seconds, cancel the intermediate units, and you're left with the correct units!
Code: Select all
1 year | 365 days | 24 hours | 60 minutes | 60 seconds
       |     year |      day |      hours |     minute

Everything but seconds cancels out, and simplify to 31,536,000 seconds!

I hope this help.
William J. Knight
Health Physicist
Los Alamos National Labs
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Joined: Tue Jan 13, 2004 9:43 pm
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