Discussion in 'Mathematics and Physics' started by PG1995, Apr 10, 2015.

1. ### PG1995Active Member

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Hi

I was just curious to find out that how a gas meter is read and how the total bill is calculated. The meter installed at home is Sensus CubixRS G4 (here is the datasheet).

Q1:
Let's have a look on a picture of related gas meter below. (source)

i: If you see the specs of Sensus CubixRS G4, it says that cyclic volume is 1.20 dm3. It would mean that a cycle is completed for a flow of 1.20 dm3. Here, the cycle would mean that the right most disk on meter with the digits 0 through 9 moves from "0" to "0" to complete one cycle. Do you agree with me?

ii: I believe that the first three disks from the right shown between red outline use the unit of dm3. The rest of five disks use the unit of m3. There are 1000 dm3 in 1 m3. Do you agree?

iii: Suppose the meter reads 1000. Would you read it as 1 m3 or 1.2 m3? I would say that it should be read 1.2 m3 because the flow of 1.2 dm3 corresponds to one complete cycle therefore when 1000 cycles are completed, it would translate into 1200 dm3 or 1.2 m3. What do you say?

iv: The meter says that Pmax=75 mbar. I would interpret it to mean that maximum pressure of gas sustained by the meter is 75 mbar.

The figure of 75 mbar is too low. Standard atmosphere pressure is taken to be 101325 Pa or 1.01325 bar. Generally, two distinctions are made with given pressure. Pounds per square inch absolute (psia) is used to make it clear that the pressure is relative to a vacuum rather than the ambient atmospheric pressure. Since atmospheric pressure at sea level is around 14.7 psi, this will be added to any pressure reading made in air at sea level. The converse is pounds per square inch gauge or pounds per square inch gage (psig), indicating that the pressure is relative to atmospheric pressure. For example a bicycle tire pumped up to 65 psi above atmospheric pressure, will have a pressure of 65 + 14.7 = 79.7 psia or 65 psig.

I would say that the gas has higher pressure than the ambient atmospheric pressure therefore it's possible that Pmax should be read as "1.01325 bar + 75 mbar". What do you say?

Q2:
i: The unit used for billing is hm3 where 1 hm3 = 1000000 m3 (use this calculator for conversion). Last month we consumed 138 m3 as shown on the bill. A general thumb of rule to find hm3 is to divide number of cubic meters by 100 as I was told by a person who has worked for a gas company. So, 138 m3 would translate into 1.38 hm3. I don't even get how this rule of thumb for conversion works. Could you please help me?

ii: On the other hand, the bill didn't read 1.38 hm3 instead it was given 1.417 hm3. Now I don't even know how this number of 1.47 is calculated. But note that the bill does use some pres./factor and temp./factor where pres./factor=0.39/1.0266 and temp./factor is blank.

I do have some other questions but I believe that first I should clear the ones above. Thank you for your help.

Best wishes
PG

1: http://en.wikipedia.org/wiki/Gas_meter
2: http://metricunitconversion.globefeed.com/Volume_Conversion.asp (extensive calculator for volume calculations)

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2. ### JimBSuper ModeratorMost Helpful Member

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No.
The meter is a diaphragm/bellows type meter, the first type in your wiki link.
One cycle is the bellows mechanism filling and emptying one time.

Yes and no.
The black digits are in cubic metres, the red digits are parts of a cubic metre.
So 123.456 is just plain 123.456m^3.

The little "d" prefix is "deci" just like in deciBel.
So there are 10 dm^3 in one m^3.

I say that 1.000 is 1m^3 for the reasons discussed above.
Therefore 1000 meter cycles is 1.2m^3

Correct.

The 75mbar is GAUGE pressure relative to the ambient (atmospheric) pressure.
Atmospheric pressure varies with location and weather.
The max pressure of the meter is 75mbar above whatever the air pressure is.

Wrong.
The little h is "hecto", 100 times.
So 1hm^3 is 100 m^3.

I do not know what these factors are in relation to this type of meter, but....
1.38 x 1.0266 = 1.417

JimB

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3. ### PG1995Active Member

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Thank you, JimB.

So, they are using deci- differently. Generally, there are always 1000 dm^3 in 1 m^3.

I believe that by meter cycles you are referring to internal cycles where one cycle is the bellows mechanism filling and emptying one time. I was talking about meter counter cycles where one disk has numbers from 0 thru 9.

Again, they are using it differently because normally there are 1000000 hm^3 in 1 m^3.

Someone else might shed some light on this. But let's talk about pressure factor and why it is needed.

Gas meters measure a defined volume, regardless of the pressurized quantity or quality of the gas flowing through the meter. Temperature, pressure and heating value compensation must be made to measure actual amount and value of gas moving through a meter.[1]

If some place is located at a higher altitude compared to base station of a gas company then the gas need to be pumped more vigorously or need to be pressurized more so that the gas could reach customers at usable pressure.

It should be noted that the altitude for a certain place is an average value. Suppose that a city has an altitude of 300 meters. In the same city there would be places which are quite below the 300 meters mark and some places are well above the 300 m mark.

In this document read the section "Meters operating at elevated pressures" to the point where it says "at the burner tip". It is written that if the meter is operating at 1 PSIG or above then pressure factor should be used. The example says that the meter is operating @ 2 PSIG. (Sorry, I have lost my thread of thought. Why doesn't gas company supply @ <= 1 PSIG )

Q3:
Your gas bill will also probably list GCV value. GCV stands for "Gross Caloric Value" and has a unit of BTU/SCF.

This page lists caloric value for different substances. The caloric value of natural gas or methane should lie somewhere between 911 and 1012. This page explains the difference between gross caloric value and net caloric value.

The British thermal unit (BTU or Btu) is a traditional unit of energy equal to about 1055 joules. It is the amount of energy needed to cool or heat one pound of water by one degree Fahrenheit (Physical analogue; one four inch, wooden kitchen match consumed completely generates 1 BTU). A temperature difference of 1°F is the equivalent of a temperature difference 0.556°C. Therefore, it can be written that one BTU is the amount of energy needed to cool or heat one pound of water by 0.556°C.

SCF stands for Standard Cubic Feet. A standard cubic foot of gas is defined as a cubic foot at a temperature of 21 ºC (70 ºF) and a pressure of 101.35 kilopascals (14.696 psia)". [1][2] Other base pressures and temperatures are sometimes used as well.[2]

Suppose, your bill shows that the gas consumed is 138 m^3 and pressure factor is 1.0266. After pressure factor correction, we have 141.6708 m^3 or 1.417 hm^3. After converting 141.6708 m^3 into cubic feet, we have 5003.06 ft^3. Let's assume that there are 913 BTU/SCF. The total number of BTU consumed is 4557784.927. After converting BTU into MMBTU, we have 4.557785 MMBTU. You might be billed like \$2/MMBTU or \$0.5/MMBTU.

Regards
PG

1: http://en.wikipedia.org/wiki/Gas_meter#Diaphragm.2Fbellows_meters
2: http://en.wikipedia.org/wiki/Standard_cubic_foot
3: http://www.thefreedictionary.com/Offtake
4: http://en.wikipedia.org/wiki/British_thermal_unit#For_natural_gas
5: http://en.wikipedia.org/wiki/Natural_gas#Energy_content.2C_statistics.2C_and_pricing
6: http://www.wikinvest.com/wiki/MmBTU
7: http://www.rapidtables.com/convert/energy/kWh_to_BTU.htm
9: http://www.crmu.net/PDF files/Rates/Natural Gas/Pressure Factor Adjustment Rate Schedule.pdf

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5. ### JimBSuper ModeratorMost Helpful Member

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No, THINK!

There are 10 deci-metres in a metre.
The volume of a cube with sides 1dm, is 10^-3 m^3, a cubic deci-metre.
BUT, a deci- cubic metre is 0.1 cubic metres.

One cubic deci-metre is not the same as one deci- cubic metre.

JimB

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6. ### Tony StewartWell-Known MemberMost Helpful Member

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1 dm³ = 1000000 mm³
1 dm³ = 1000 cm³
1 dm³ = 0.001