Some sums.

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tapkaJohnD

Original Poster:

1,945 posts

205 months

Saturday 10th October 2015
quotequote all
I'm trying to reconcile two ways of estimating the capacity needed for a fuel pump.
The example is a rally Mini (original type, of course):

1/ A rally Mini in stage is likely to have an overall consumption of 12 miles per gallon, and an average speed of up to 75miles per hour. A stage of 37 miles (rather long, but it will ease calculation) takes 30 minutes to complete and consume 3 gallons of fuel, a rate of 6 gallons an hour.

2/ But average fuel consumption is not peak consumption. How much will the Mini use at full power and revs?
Maximum safe revs for Mini Copper S - ?6500rpm
Capacity – 1293mls
The full capacity is only pumped by the engine once per two revolutions
So engine gas flow at max revs = 1293 x (6500/2) mls
= 4,202,250mls/minute or 4202.25 litres/min
1 gram of air occupies 22.4 litres so the mass of this air will be 187.6 grams
At maximum acceleration, assume mixture richer by 25% on ideal of 15:1 air:fuel by mass, so 11.25:1
so at that mixture, 188gms mass of air will burn 16.7 grams of fuel per minute

Specific gravity of petrol is 0.737gms/ml
So that mass of fuel burnt per minute will have a volume of 23 mls (rounded to whole mls)
So in the 30 minute stage example above it will consume 23x30mls= 679mls

And in one hour, 1358mls, or approx 0.3 gallons.

Solution 1 matches reality, but solution 2 is ridiculous.
I'd like to be able to show that both are in the ballpark.
Where am I going wrong?
JOhn

tapkaJohnD

Original Poster:

1,945 posts

205 months

Sunday 11th October 2015
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Thank you!
My error was to say, "1 gram of air occupies 22.4 litres" No! That would be true of Hydrogen!
Air is a mixture of gases, mostly nitrogen, with 21% oxygen, which is unhelpful as mixtures are always in AIR:Fuel ratios.
But I am reliably informed that the mean gram-molecular weight of air is 29.

Avogardro's Number, 22.4, is the number of atoms or molecules in one 'mole' of a substance.
It describes the volume (at normal temperature and pressure) of one gram-molecular weight of a gas.
This is counter-intuitive, as it would seem logical that a larger molecule would occupy more space, but for instance the volume of a 'mole' of water vapour is the same as a mole of oxygen, and a mole of hydrogen, and half that of the two moles that went to make it! But it weighs more.


So, Reworking Method 2/

Maximum safe revs for Mini Copper S - ?6500rpm
Capacity – 1293mls
The full capacity is only pumped by the engine once per two revolutions
So engine gas flow at max revs = 1293 x (6500/2) mls
= 4,202,250mls/minute or 4202.25 litres/min
29 grams of air occupies 22.4 litres so the mass of this air will be 5440 grams
At maximum acceleration, assume mixture richer by 25% on ideal of 15:1 air:fuel by mass, so 11.25:1
so at that mixture, 5440 gms mass of air will burn 484 grams of fuel per minute

Specific gravity of petrol is 0.737gms/ml
So that mass of fuel burnt per minute will have a volume of 356 mls (rounded to whole mls)
So in the 30 minute stage example above it will consume 356x30mls= 10692 mls

And in one hour, 10.7 litres, or approx 2.35 gallons.
At least that result is in the same units as Method 1!

It's obvious that, especially at high revs, the dynamics of the engine will mean that it will ingest less than the capacity times half the revs, but that ratio is unknown to me.
And whatever the fuelling method, it's air flow that governs the amount of fuel put into it.
Yes, the air/fuel mix will have a greater mass, but Avogardro's Number will still be the same!
So I don't think that it will have a great effect on the result.

Thanks again! I'm delighted to found at least one error, correcting which puts the result into reality, and it was getting your reaction that found it!
It's good to talk, innit?

John

tapkaJohnD

Original Poster:

1,945 posts

205 months

Friday 16th October 2015
quotequote all
The Oracle has spoken!

Dear John,

Protected, does not necessarily mean it has to be covered. It would be considered protected if the fuel lines were routed in such a way that there is no risk of damage. However if they are routed though vulnerable areas such as footwells, then a cover using a material of enough strength to prevent the pipe being crushed or damaged will meet the regulation.

Best Regards
Michael


Michael Duncan
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tapkaJohnD

Original Poster:

1,945 posts

205 months

Tuesday 20th October 2015
quotequote all
Sorry to confuse!
I posted the reply in the wrong thread. See: http://www.pistonheads.com/gassing/topic.asp?h=0&a...
John