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# Fuel consumption

## Question

In Europe, we measure the fuel consumption in litres per 100 km. It is quite convenient because I can easily figure out what a litre is (a little bit less than one and half standard wine bottle) and it is not hard to figure out a distance of 100 km. However, any teacher of physics would point out that volume should be measured in [m3] and distance in [m]. After simplification, I get that fuel consumption should be measured in [m2]. What does it represent?

In the U.S., the consumption is measured in miles/gallon. Quite convenient, too, just that in the MKSA system, I get [1/m2]. How do you represent that?

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Let A = (volume of consumed fuel) / (distance traveled consuming the fuel)

Then A is the area, perpendicular to the direction of travel, that sweeps out a volume equal to the consumed fuel as the vehicle moves forward.

A gets bigger when you accelerate, smaller when you coast.

In the U.S. scenario, if you poured fuel into a tank with cross section A, the fuel would rise to a height in that tank equal to the distance the vehicle would travel in consuming that fuel..

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Though correct, a little wordy. Can you imagine a physical object fitting this definition?

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Sure. Rectangular Parallelepiped

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"Rectangular Parallelepiped"s are usually not used to transport fuel.

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when I first started mulling this over, I realized that miles/ gal or km/ liter are skipping several steps.

We really mean that gal of gas is sufficient to propel this vehicle so many miles.

I took a typical value for a US car [25 mpg] and started converting it.

Values are approx

25 miles ~ 32 km

1 Gal ~ 3.7 Liters ~ 3.7/1000 Meters 3

25 Mile/ gal = 32 km/ 0.0037 meters 3 ~ 32,000/ 0.0037 /meters 2

therefore 25 miles/ gal ~ 118,400,000 /meter 2

I am at a loss for how this related to the parallel piped, though I cannot find anything else that makes sense.

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when I first started mulling this over, I realized that miles/ gal or km/ liter are skipping several steps.

We really mean that gal of gas is sufficient to propel this vehicle so many miles.

I took a typical value for a US car [25 mpg] and started converting it.

Values are approx

25 miles ~ 32 km

1 Gal ~ 3.7 Liters ~ 3.7/1000 Meters 3

25 Mile/ gal = 32 km/ 0.0037 meters 3 ~ 32,000/ 0.0037 /meters 2

therefore 25 miles/ gal ~ 118,400,000 /meter 2

I am at a loss for how this related to the parallel piped, though I cannot find anything else that makes sense.

Well, I think that you have to add units to the numerator (as well as the denominator) to make any sense of things.

in your example, 25 miles/gal = 118,400,000/m2=118,400,000 parsecs/parsecs-m2. Now that makes physical sense!

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not sure what to make of

"Well, I think that you have to add units to the numerator (as well as the denominator) to make any sense of things.

in your example, 25 miles/gal = 118,400,000/m2=118,400,000 parsecs/parsecs-m2. Now that makes physical sense!"

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not sure what to make of

"Well, I think that you have to add units to the numerator (as well as the denominator) to make any sense of things.

in your example, 25 miles/gal = 118,400,000/m2=118,400,000 parsecs/parsecs-m2. Now that makes physical sense!"

What I was getting at is that 118,400,000 is missing an interpretation in units (in this case, units of length). Any unit of length (including parsecs) would work.

So, for example, we could write 118,400,000 m/m3, where the units in the denominator refer to fuel. But writing 118,400,000/m2 doesn't even hint

that the numerator should represent distance and the denominator should represent fuel volume. I'll grant you that parsec-m2 is a rather strange unit of volume.

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Let A = (volume of consumed fuel) / (distance traveled consuming the fuel)

Then A is the area, perpendicular to the direction of travel, that sweeps out a volume equal to the consumed fuel as the vehicle moves forward.

A gets bigger when you accelerate, smaller when you coast.

In the U.S. scenario, if you poured fuel into a tank with cross section A, the fuel would rise to a height in that tank equal to the distance the vehicle would travel in consuming that fuel..

You got the first part to 97% - I wanted to hear "section of a pipeline along the trajectory". The tank of the U.S. scenario corresponds quite well to the pipeline, just the section of a tank is not measured in 1/m2, so the second part of the problem is still open.

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I asked some others and after talking it over, I realized that we cannot mix m [distance] with m3 of volume.

The m/ m3 is actually shorthand for m / m3 of fuel.

Dividing through would leave the expression 1/ m2 of fuel.

Bottom line: I think this was a trick question.

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