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# I need to know the conversion equation to convert jet fuel

I need to know the conversion equation to convert jet fuel from liters to kilograms.
What is the difference between the 2 fractions 1.77 L/1kg. and 1L/1.77kg when it comes to conversions?
Lastly, 22,300 kg equals how many Liters

Hi,

Thank you for using the site.

To convert from liters to kilograms you would need to know the density of the fuel. There are several different types of jet fuel though, and the densities vary by type. Is there a particular type that you are interested in?

Ryan

Hi again,

As an example, Jet-A fuel is used in the US and has a density of 0.820 kg/L.

To convert a volume of this fuel in liters to a mass in kilograms, you would multiply the volume by the density:

mass = volume * density

So let's say that you need 1000 L of this fuel. The mass would then be:

mass = (1000 L)(0.820 kg/L) = 820 kg

So, in general, you would only need to multiply the volume (in liters) by the density (in kg per liter) to get the mass in kilograms.

The fraction 1.77 L/1 kg implies that each kilogram occupies 1.77 liters, or that it takes 1.77 L to equal 1 kg in mass.

The fraction 1L / 1.77 kg implies that each liter has a mass of 1.77 kg.

Neither of those fractions is in the form that you need if you wish to convert from liters to kilograms. (Actually, you could do it by dividing by the fraction instead of multiplying, but that tends to get complicated and invites mistakes. It's better to have the proper units on the conversion factor so that you can just multiply values together directly.)

Assuming that we are still considering Jet-A fuel, then converting 22,300 kg into liters would look like this (and here we will divide by the conversion factor):

(22,300 kg) / (0.820 kg/L) = 27,195.12 L

You could also do this conversion by using the reciprocal of the density:

(22,300 kg)(1.219512 L/kg) = 27,195.12 L

Thanks,

Ryan

Customer: replied 8 months ago.

The problem didnt say, just that it was fuel placed in the fuel tanks. I have to show my work. Jet fuel placed in 767 jetliners. I have to show the mistake in calculationa by the ground crew who measured 7,682 liters in tank, and were trying to find how many mire liters needed to get 22,300 kilograms. The crew felt that yoy multiply the numbers of liters the weight of the liter. With the conversion being 1.77. I had to explain the difference in the two equations I gave you. I hope this helps.

Ok, I didn't realize that this was a problem from a textbook, as opposed to a general interest question.

Can you take a picture or screenshot of the problem and send that so that I can read exactly what the problem statement gives?

Thanks,

Ryan

A little bit of research has revealed that this seems to be in reference to the "Gimli Glider" incident in 1983.

In that incident, the issue was that the 1.77 conversion factor was in units of pounds per liter, instead of kilograms per liter. As a result, the crew had about half as much fuel as they thought they had: 10,115 kg, instead of 22,300 kg. This is because their calculations provided them with 22,300 pounds of fuel, instead of 22,300 kilograms.

Fortunately, nobody was seriously injured (miraculously, since they were forced to land at an airfield that was hosting drag races at the time and was full of spectators). Still, the incident serves as an important reminder of how important math can be, and how a relatively simple mistake can have potentially disastrous consequences.

Please let me know if there is anything else that I can do to help.

Ryan

Customer: replied 8 months ago.

Yes. The assignment is based on Flight 143.

One of the questions was to calculate the amount of fuel in liters and kilograms that should have been added to ensure the plane was safe.

Also, how would the two fractions 1.77L/1Kg and 1L/1.77kg differ in making a conversion?

Thank you so much, I was so confused. I have no mathematical abilities.

Hi,

Ok, no problem.

The error made when fueling Flight 143 was that the conversion factor used was in units of pounds/liter, when it should have been in kg/liter. The correct conversion factor would have been:

(1.77 pounds/L)(0.45359 kg/pound) = 0.803 kg/L

Assuming that the measurement of 7,682 liters was correct, the mass of fuel in the tanks at that time would have been:

(7682 L)(0.803 kg/L) = 6,168.646 kg

The amount that would need to be added to get the plane's fuel load up to 22,300 kg is then:

22,300 kg - 6,168.646 kg = 16,131.354 kg

The volume (in liters) that should have been added at that point is then:

(16,131.354 kg) / (0.803 kg/L) = 20,088.86 L

Regarding the two fractions, both 1.77 L / 1 kg and 1 L / 1.77 kg would have been the incorrect factor to use, because the 1.77 value is part of the conversion from pounds to liters, instead of from kg to liters. Ignoring the value and instead just focusing on the units of the two fractions, the fraction 1.77 L / 1 kg would mean that each kilogram of fuel occupied a volume of 1.77 liters. The fraction 1 L / 1.77 kg means that each liter has a mass of 1.77 kg.

To look at the fractions another way, 1.77 L / 1 kg is equivalent to 1.77 L/kg, while 1 L / 1.77 kg is equivalent to 0.565 L/kg. Clearly the two factors are very different values.

Both fractions could be used to convert from kg to liters, so it would just be a matter of which value was the correct factor. In the case of Flight 143 though, neither of those factors would have been correct.

I hope this helps.

Thanks,

Ryan