Calculating the BTU output of a torch, or single hole orifice.
BTU output is the number of cubic feet of gas coming through an
orifice, times the number of BTU's per cubic foot over time.

Cubic feet of gas through the orifice is:
Pressure differential, Hole size (area), Hole coefficient (how a thin
stream flows through a hole. This will be different for a hole under a
minimum size or over a maximum size, specific gravity (and maybe
viscosity of the gas).

We are calculating the cubic feet (moles, since a mole of any gas
occupies the same volume under standard pressure and temperature. ) of
gas that comes through a hole at each PSI (atmosphere being 0 for the
differential).

We are assuming that we get enough air (20% oxygen, Nitrogen mix) to
fully combust the fuel.

Starting with the diameter we need the area of the hole in inches.

A .04 inch hole has a surface area of PI * R Squared. Radius of .04
inch hole is: .02 PI * .02 = 0.0628318 squared = 0.00394783509124 sq
inches.

Now we have the square inches of area for the hole.

At pressure for the density of the gas how much goes through in a
given timespan?

( ((3.14159 * (Dia/2) Squared) * Coeff/144)
Therefo
((PI * Diameter / 2) Squared) * (Coefficient / 144) * (21407 * (sqroot
of PSI)) * BTUperCubicFoot * 60

After entering the new formula into the calculator, guess what!
It does not match the chart in the Berquist book
(or any other standard table for orifice capacity that we can find.)!

After fooling around with the Coefficient / 144 figure,
"430" makes it match the chart almost exactly for all hole sizes and
pressures.

How much air do we need?
The combustion reaction always has these these components:
fuel molecules + O2 -- CO2 + H2O.

A Mole is a Mole.

Knowing that a mole of any gas at standard pressure and temperature
occupies the same amount of space tells us that we can use the
calculated mole number of oxygen for each fuel to determine how many
cubic feet of oxygen we need for combustion.

For example: One mole of Methane needs two moles of Oxygen
for complete combustion (see the chart).

So one Cubic Foot of Methane needs two cubic feet of oxygen.

One Cubic foot of Propane needs Five Cubic feet of oxygen.

The only Wrinkle here is that Hydrogen, for example is 2 molecules
using 1 molecule of O2,
so the actual figure is .5 for One molecule.

Woodgas, Acetylene, Butane, Diesel, are all molecules that don't work
out unless you use two molecules instead of one for the calculations.

These end up being actually half of the stated figure for oxygen when
thinking of one molecule.

Air has 20% oxygen per volume. So 5 / .2 = 25.

Propane needs 25 cubic feet of air per cubic foot of Propane at
standard pressure and temperature.

The other thing that you will notice is that vs BTU the fuels need for
air doesn't seem to make sense unless you take into account the
elemental make-up of each fuel.

If your fuel is predominently Carbon then it needs only one Oxygen,
but if your fuel is predominently Hydrogen then it needs TWO Oxygen
atoms to combust as the products of combustion are either CO2 or H2O
(or both in varying qtys).

http://www.frostic.com/software/BTUcalcu/index.htm

wrote:
Calculating the BTU output of a torch, or single hole orifice.

Why this complicated approach instead of just a simple empirical test:
Weigh the cylinder, burn the torch for let's say 15 minutes, weigh the
cylinder again, and multiply by 4 to get the hourly consumption.
Multiply by 12,874kWh/kg (the heating value of Propane), convert into your
BTU, and you are all set.

jue

Jürgen Exner wrote:
wrote:

Calculating the BTU output of a torch, or single hole orifice.


Why this complicated approach instead of just a simple empirical test:
Weigh the cylinder, burn the torch for let's say 15 minutes, weigh the
cylinder again, and multiply by 4 to get the hourly consumption.
Multiply by 12,874kWh/kg (the heating value of Propane), convert into your
BTU, and you are all set.

jue




Yes, heating values for various gases are readily available from tables.
The problem I see with any method you use is the assumption that you
have 100% propane, you don't, unless you're buying 'research grade' or
'chemical grade' propane. Common 'propane', as supplied for home
heating, can contain a significant amount of butane depending on source,
season, and location. There will also be a possibly significant amount
of the other light hydrocarbons both lighter and heavier than propane.
Propane as purchased in small cylinders for torches for sure has other
gases in it to some degree or another, but it could be purer than that
sold for heating.

If your calculated values need to be exact an analysis of the fuel in
question is needed. Then knowing the fractions and BTU content of the
various components the overall BTU content can be calculated. This may
or may not be overkill for your application.

As an aside fuel gases vary widely in composition and to compare blends
to insure comparable performance in appliances something called the
Wobbe Index or WI of the blend in question is determined. The Wobbe
Index of a particular gas is the BTU content divided by the square root
of the specific gravity. Blends with similar WI's will behave the same
at a common pressure and flow regardless of chemical composition.

There are two common methods to determine WI, the simplest is the
calorimeter, a device that measures the output of a thermocouple
suspended above a flame of the fuel in question supplied at a precisely
controlled pressure and temperature. Most calorimeters also have a cell
to measure the fuel's specific gravity to supply the other variable in
the equation. The other method is via gas chromatography to determine
the actual makeup of the fuel in question. The fuel's overall BTU
content and specific gravity is then calculated using the component
gases' BTU values and specific gravities supplied as constants. Both
these methods can be done 'online' more or less continuously.

The above is probably more than you want to know but you might find it
interesting. For more on the subject:

http://en.wikipedia.org/wiki/Wobbe_index

Regards
Paul
--
-----------------------------------------
It's a Linux world....well, it oughta be.
-----------------------------------------

On Aug 22, 9:16 pm, Paul wrote:
Jürgen Exner wrote:
wrote:

Calculating the BTU output of a torch, or single hole orifice.

Why this complicated approach instead of just a simple empirical test:
Weigh the cylinder, burn the torch for let's say 15 minutes, weigh the
cylinder again, and multiply by 4 to get the hourly consumption.
Multiply by 12,874kWh/kg (the heating value of Propane), convert into your
BTU, and you are all set.

jue

Yes, heating values for various gases are readily available from tables.
The problem I see with any method you use is the assumption that you
have 100% propane, you don't, unless you're buying 'research grade' or
'chemical grade' propane. Common 'propane', as supplied for home
heating, can contain a significant amount of butane depending on source,
season, and location. There will also be a possibly significant amount
of the other light hydrocarbons both lighter and heavier than propane.
Propane as purchased in small cylinders for torches for sure has other
gases in it to some degree or another, but it could be purer than that
sold for heating.

If your calculated values need to be exact an analysis of the fuel in
question is needed. Then knowing the fractions and BTU content of the
various components the overall BTU content can be calculated. This may
or may not be overkill for your application.

As an aside fuel gases vary widely in composition and to compare blends
to insure comparable performance in appliances something called the
Wobbe Index or WI of the blend in question is determined. The Wobbe
Index of a particular gas is the BTU content divided by the square root
of the specific gravity. Blends with similar WI's will behave the same
at a common pressure and flow regardless of chemical composition.

There are two common methods to determine WI, the simplest is the
calorimeter, a device that measures the output of a thermocouple
suspended above a flame of the fuel in question supplied at a precisely
controlled pressure and temperature. Most calorimeters also have a cell
to measure the fuel's specific gravity to supply the other variable in
the equation. The other method is via gas chromatography to determine
the actual makeup of the fuel in question. The fuel's overall BTU
content and specific gravity is then calculated using the component
gases' BTU values and specific gravities supplied as constants. Both
these methods can be done 'online' more or less continuously.

The above is probably more than you want to know but you might find it
interesting. For more on the subject:

http://en.wikipedia.org/wiki/Wobbe_index

Regards
Paul
--
-----------------------------------------
It's a Linux world....well, it oughta be.
-----------------------------------------

Well, Yes if you are trying to get exact figures there are always real
world wrinkles in any calculation. If though, you are building a
burner or other device and know that you need something to base your
design on you can use this calculator to estimate the requirements
needed to achieve the necessary btu with given fuel, pressure, and use
it to determine your hole size and air intake size needed...

Obviously any calculator will assume perfect conditions, i.e. pure
propane, i.e. wood gas = CO (actually is a mixture of CO, H2, various
other chemicals, etc... ) but the point is that just like a tape
measure, or a building plan this gives you something to start from.

It's kind of hard to do an empirical test, when you haven't yet built
your burner. How many prototypes do you want to go through before you
get it right.... ???

It is common practice to model an assembly on computer before actually
putting together a project. This increases production and reduces
development cost.

"Weigh the cylinder, burn the torch for let's say 15 minutes, weigh
the
cylinder again, and multiply by 4 to get the hourly consumption.
Multiply by 12,874kWh/kg (the heating value of Propane), convert into your
BTU, and you are all set."

That sure sounds like a lot of steps compared to simply entering some
figures into a calculator and having it spit out a close number...
though it would be a great way to verify your build, it certainly cant
be done until you have finished your first prototype. Not to mention
the waste of fuel and time compared to using the calculator.

Another thing is that your figures will not be 100 percent accurate
either, because of the mix of propane that you have, errors in timing,
weighing errors and other factors that include human error, this
method is probably not intrinsically any more accurate than estimating
it with a handy calculator...

Best regards,

Chris Frostic
www.frostic.com