<<Mathematics, Calculations and Supporting Data>>

EnviroEngr · Last edited by EnviroEngr on Tue Mar 01, 2005 5:58 pm; edited 1 time in total

I am more often seeing various arguments referencing a need for showing traceability, 'numerical reproducibility' and, in short, proof.

I'm biased in that particular way myself and fully support such a call for factual accountability where it applies. Ergo, I offer this thread as a reminder to do the homework of substantiating claims that can or already do follow principles of mathematics and/or logic. To this end, I can begin providing the standard algebraic or differential equations and conversion tables that will be needed to demonstrate the theoretical or empirical validity of certain assertions; AND this thread can be used as electronic scratch paper and a notepad for showing how a given conclusion was reached.

Character assassinations and pointless bickering over whose viewpoint is more right or wrong are about as useless as an umbrella made out of 1-inch-square wire mesh. Heated debates over whose equations model reality more accurately, on the other hand, would get us at least a little closer to a run of thinking that may actually prove useful in a powerdown scenario.

Given the relevance and applicability of this thread, I (or someone) may move it to another place.
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Webster Hubble Telescope · Guest

I really dig this message board; it demonstrates how contributors aren't afraid to do the math, so to speak.

Here is my small contribution as an "Energy Illiteracy" test (Paul Roberts has been bandying about the illiteracy aspects recently). I have my own answers, if needed , but here goes:

1. If humans could metabolize petroleum, how much volume would they need to consume per day to maintain the average caloric intake (say 2500 calories)?

2. How many SUV's can be operated continuously (travelling 60 MPH) via the oil output of one average stripper well in the USA?

3. Which is greater: (a) The flow of water in the Colorado River at Lees Ferry, AZ or (b) the worldwide production of oil (flow that is)?

4. How much vegetable/cooking oil gets wasted by the average person per day?

http://mobjectivist.blogspot.com

EnviroEngr · Posted: Fri Jul 02, 2004 10:42 am Post subject: Move

Do you want this back over on the Modeling Forum?
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EnviroEngr · Posted: Fri Jul 02, 2004 11:52 am Post subject: Moved

I'll answer that.

Now to retry some functionality to make sure it's still good to go...
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EnviroEngr · Posted: Fri Jul 02, 2004 12:00 pm Post subject: The Greek Alphabet

The Greek Alphabet

Αα
Ββ
Γγ
Δδ
Εε
Ζζ
Ηη
Θθ
Ιι
Κκ
Λλ
Μμ
Νν
Ξξ
Οο
Ππ
Ρρ
Σσ
Ττ
Υυ
Φφ
Χχ
Ψψ
Ωω

pi looks anemic. The rest looks good.
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| Whose reality is this anyway!? |
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EnviroEngr · Posted: Fri Jul 02, 2004 12:15 pm Post subject: Math Symbols 1

Now the first symbol set:

±≤≥∝÷〈〉∼≈∈∩∑∞→←↔∘∙°µ∫∏∓∇∂ ʹ ʺ ℯℓℏℑℜ⇄⇒⇔∮ℭ℘ʅℂ

Second set:

⌠⌡√

Basic Set Theory:

∪ ⊂ ⊃ ⊆ ⊇ ∍ ∅ ⇒ ⇐ ⇔ ≠ ≢ ∷ ≃ ≅ ∃ ∀ ⊊ ⊋

The limitations are many.
Can work around that.
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EnviroEngr · Posted: Fri Jul 02, 2004 12:16 pm Post subject: Equations

Did a Diffy Q, know it works...
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EnviroEngr · Posted: Sun Jul 04, 2004 6:10 pm Post subject: Conversion Table 1

Simple Conversions

VOLUME

1 mL = 0.0338 Oz
1 L = 0.2642 Gal

1 Oz = 29.5735 mL
1 Gal = 3.7850 L

* 1 Gal = 231.0 Cu. In.
* 1 Gal = 0.1337 Cu. Ft.
* 1 Cu. Ft. = 7.48 Gal

LENGTH

1 mm = 0.03937 in
1 in = 25.40 mm

1 cm = 0.3937 in
1 in = 2.54 cm

1 m = 3.28 ft
1 ft = 0.3048 m

1 km = 3280.84 ft
1 ft = 0.0003048 km

1 km = 0.62137 Mi
1 Mi = 1.609344 km

* 1 Mi = 5280.0 ft

WEIGHTS

1 gm = 0.03527 oz
1 oz = 28.3495 gm

1 kg = 2.20462 lb
1 lb = 0.4536 kg

TEMPERATURE

(Temp(F) - 32) x 5/9 = Temp(C)
Temp(C) x 9/5 + 32 = Temp(F)
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| Whose reality is this anyway!? |
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(-------< Temet Nosce >-------)
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EnviroEngr · Posted: Sun Jul 04, 2004 6:18 pm Post subject: Up and Down

Exponents and subscripts are going to be something of a challenge. Maybe by using {Code} or something similar, I can work it out.

If anyone has any ideas, let me know.

Thanks.

{I can either PDF or JPG MathCad screen catches. If I can do that, I can post equation runs in native symbol format as graphics; that is, if Aaron can help me put them up. Thanx Aaron.}
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| Whose reality is this anyway!? |
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EnviroEngr · Posted: Wed Jul 07, 2004 2:53 pm Post subject: Gauss/Laplace

This is going to look a little goofy, but here it goes:

Function
F(x) = 1/(2π)^0.5(e^(-x^2/2))
Read like this: Function of x equals one over the square root of 2 pi times e raised to the negative one half x squared.

First Derivative
F'(x) = -x/(2π)^0.5(e^(-x^2/2))

Second Derivative
F"(x) = (x^2-1)/(2π)^0.5(e^(-x^2/2))

Finding the relative minima and maxima on both the First and Second Derivative curves makes identifying the inflection points of the Function curve really easy, especially if all three 'functions' are graphed together.

π = pi
^ = exponent follows
e = Inverse Natural Log of 1

I will talk to Admin to see if I can get Math Symbols/Layout functionality (or something approximating it) in here. This is do-able but sufficiently cumbersome to warrant looking for better presentation techniques.
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| Whose reality is this anyway!? |
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(-------< Temet Nosce >-------)
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small_steps · Posted: Wed Jul 07, 2004 3:55 pm Post subject: Energy Units/Conversions

Energy Units and Conversions

A BTU (British Thermal Unit) is the amount of heat necessary to raise one pound of water by 1 degree Farenheit (F).
1 Joule (J) is the MKS unit of energy, equal to the force of one Newton acting through one meter.
1 British Thermal Unit (BTU) = 1055 J (The Mechanical Equivalent of Heat Relation)

Power = Current x Voltage (P = I V)
1 Watt is the power from a current of 1 Ampere flowing through 1 Volt.
1 kilowatt is a thousand Watts.
1 kilowatt-hour is the energy of one kilowatt power flowing for one hour. (E = P t).
1 kilowatt-hour (kwh) = 3.6 x 106 J = 3.6 million Joules

1 calorie of heat is the amount needed to raise 1 gram of water 1 degree Centigrade.
1 calorie (cal) = 4.184 J
(The Calories in food ratings are actually kilocalories.)

1 BTU = 252 cal
1 Quad = 1015 BTU (World energy usage is about 300 Quads/year, US is about 100 Quads/year in 1996.)
1 therm = 100,000 BTU

Power Conversion

1 horsepower (hp) = 745.7 watts
Gas Volume to Energy Conversion
One thousand cubic feet of gas (Mcf) -> 1.027 million BTU = 1.083 billion J = 301 kwh
One therm = 100,000 BTU
1 Mcf -> 10.27 therms
Energy Content of Fuels
Coal 25 million BTU/ton
Crude Oil 5.6 million BTU/barrel
Oil 5.78 million BTU/barrel = 1700 kWh
Gasoline 5.6 million BTU/barrel (a barrel is 42 gallons)
Natural gas liquids 4.2 million BTU/barrel
Natural gas 1030 BTU/cubic foot
Wood 20 million BTU/cord

from: http://www.physics.uci.edu/~silverma/units.html

also, regarding equations:
considering MS word, do many of the members of the forum know how to use field codes?
If not, this may be useful:

http://courses.engr.wisc.edu/ecow/get/me/746/lorenz/1eqnfields_in_msword.pdf

{touch up; EE}

notacornucopian · Posted: Wed Jul 07, 2004 4:12 pm Post subject:

Don't mean to nitpick, but your value for Quads in relation to usage per year seems pretty light.....

small_steps · Posted: Wed Jul 07, 2004 4:32 pm Post subject:

notacornucopian · Posted: Thu Jul 08, 2004 8:34 am Post subject:

Nitpicker again - the value in BTU's that equal Quads just doesn't seem right - even with the update it would suggest that world usage in cubic feet of NG would be about 400 !
Is it maybe 1015 million BTU per Quad ?

EnviroEngr · Posted: Fri Jul 09, 2004 10:33 am Post subject: Symbol Library Enhancement

I propose using MimeTeX, a LaTeX-to-gif converter. see
http://www.forkosh.dreamhost.com/source_mimetex.html

I can (try to) install this into phpBB if you'd like, or I'm open to other suggestions.

Memory: Store this information.
_________________
--------------------------------
| Whose reality is this anyway!? |
--------------------------------
(-------< Temet Nosce >-------)
____________________________