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#1
08-19-2010, 12:46 PM
 Power! Guest Posts: n/a
Convert Density from slug/ft^3 to kg/m^3

Hello all,

Just as the title states, I need to convert 5.26 slug/ft^3 into SI density units, which I believe is kg/m^3. I am new at this so if someone could explain in detail I would greatly appreciate it!
#2
08-19-2010, 01:36 PM
 JohnS Double Ultimate Supreme Member Join Date: Dec 2007 Location: SE Michigan, USA Posts: 8,701 Rep Power: 17
Re: Convert Density from slug/ft^3 to kg/m^3

Quote:
 Originally Posted by Power! Hello all, Just as the title states, I need to convert 5.26 slug/ft^3 into SI density units, which I believe is kg/m^3. I am new at this so if someone could explain in detail I would greatly appreciate it!
If you are converting to the metric system, I strongly recommend NIST publications SP330 and SP811, which are free downloadable guides from the Dept. of Commerce.

The simple answer from the extensive table of conversions in the appendix of SP811 is multiply slug/ft³ x 515.3788 to get kg/m³, so 5.26 slug/ft³ x 515.3788 = 2710.9 kg/m³.

If you want to derive it, well that is a PITA. The slug is a made-up unit to rationalize F = ma in "english" units. A 1 lbf force accelerates a 1 lbm mass at g, about 32 ft/s². The slug is a made up mass such that 1 lbf force accelerates it at 1 1ft/s². The exact value comes from "standard gravity" in the metric system, 9.80665 m/s², and the definition of a foot, 0.3048 m, both exact, "g" in the english system is 9.80665 m/s² / 0.3048 m/ft = 32.17405 ft/s². So multiply by 32.17405 lbm/slug.

Then convert pounds to kilograms (0.45359237 kg/lbm), and cubic feet to cubic meters (1 ft/0.3048 m)³ serially.

5.26 slug/ft³ x (9.80665/0.3048) lbm/slug x 0.45359237 kg/lbm x (1 ft/0.3048 m)³ = 2710.9 kg/m³

Numerically the factor is 9.80665 x 0.45359237 /(0.3048)^4, those conversions are all exact, so the factor is as precise as you carry the math, 515.37882.
#3
08-19-2010, 03:30 PM
 PowerHouse Junior Member Join Date: Aug 2010 Posts: 1 Rep Power: 0
Re: Convert Density from slug/ft^3 to kg/m^3

Thanks for that extensive reply, you have helped me greatly. I appreciate the time you spent on my question.

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