problem with units

[akazimli]

Hello dear community!

I know that there were many discussions about units but I cannot find(understand) help for my issue. I am trying to put in units but failed. I need Q in Watts, W in kg/h and show C in units like it is given in API 520 I. I will be very grateful if someone can help, explain how to solve it.

Regards,

Aydan

[AlvaroDíaz]

Hi

Q in watts is not a heat, is a power, this is, how many units of heat energy flows at any second. For this case, the energy unit is Joule. Other usual unit could be BTU/hr or cal/sec. So, "correct" letter for that heat flow is "Q.dot".

Other variants of express "heat" are Q', Q'' and Q''', which usually represent heat by length, surface and volume, and the combination also, but less usual, of Q.dot', Q.dot'' and Q.dot'''

Finally, you have sometimes the convention that Q in uppercase is heat, but q could represent heat by kilogram or by mol, and the same combinations with primes and dots.

For the work and mechanical energy, have the same considerations.

W in kg/hr is bad, if W means as usual, work, and I can't interpret it as something like work, including the case that was not kg but kgf.

In many norms, as they are old, and the revisers don't want to improve so much, the conversion factors are inside the formulas, which is a very bad practice. In this cases, using mathcad, you must to take out those factors from the formulas, and rewrite them in a better form.

That seems to be the case for the formulas Q = 70900*1*Awet and W = 3600*Q/λ.

So, maybe could get better help if you put some picture of the formulation that want to use in mathcad.

Best regards.

Alvaro.

[StuartBruff]

I've just had a very brief look at the API520 ... I've passed it on to the BIPM and they are now busily putting together a SWAT team to erase the API from the face of the earth for crimes against units.   kPag? kPaa?

I think that the C coefficient should have a multiply rather than a subtract to attain some form of dimensional consistency.

Stuart

from an old National Physical Laboratory (NPL) FAQ:

What do the letters 'g' and 'a' denote after a pressure unit? (FAQ - Pressure)

The letters are meant to stand for gauge-mode and absolute-mode respectively - where a gauge-mode pressure is one normally measured with respect to ambient pressure and an absolute-mode pressure is one measured with respect to zero pressure (a more detailed explanation of pressure modes).

Despite appearing on many pressure instruments however, abbreviations such as barg, psig, kPaA, kPaG, bara, psia etcetera are not legitimate and such formatting conflicts with international written standards and good practice, and should not be used. Similarly the letters NG, ng, D or d should not be used to denote negative gauge-mode or differential-mode pressures. Where needed, the distinction should come instead through the context of use, essentially meaning that the words absolute and gauge should be printed in full next to the pressure unit - for example: bar absolute and kPa gauge. This method of formatting leaves the underlying unit intact (bar, kPa in the previous examples) and avoids implying that the unit is in some way altered by the suffix.

Part of the reason for this seemingly pedantic rule is that pressure is a quantity derived from knowledge of force and area (pressure = force/area) and none of the fundamental pressure unit definitions take the operational mode directly into account. The meanings of gauge- and absolute-mode cannot be defined as clearly and accurately as the underlying unit - for example does gauge mean 'with respect to ambient atmospheric pressure' or perhaps 'a pressure close to but not necessarily exactly at prevailing atmospheric pressure'? Is the reference pressure in an absolute mode measurement 1 000 Pa (that is about 1% of nominal atmospheric pressure - a 'good' vacuum to many people), 1 Pa, 0.0001 Pa or some other pressure? (See definition of a vacuum.) Thus there are no legitimate pressure units ending in 'a' or 'g' etc and there are never likely to be any.

Whatever pressure units you are using, if you want to follow internationally agreed and recognised conventions (recommended!) a descriptive word should be used to denote the pressure mode and not a letter.

[AlvaroDíaz]

Seems that W mean "weight". In this case, kg/hr, which is a caudal, or "gasto" in spanish, where we use g or m.dot. Also, remember that a weight is a force, so use W can cause a lot of unnecessary confusion.

See this Pentair book.

Best regards.

Alvaro.

[AlvaroDíaz]

Hi Stuart.

What can I say? This is a Pressure Relief Valve sizing program, and see the units. It uses also kPaa, in w a, and a lot of any other oddities. But this one, kg/cm^2 g it's a true joke.

One can interpret g as 9.8 m/s^2, which actually gives a correct dimension for a pressure unit, but not, for kg must to remember that this people use is as force unit (kgf) and g is for gage, which actually have not a very good translation to spanish :it must to translate as "relativa", ¿why don't use "relative" in english?. (and why don't use open questions marks?)

Best regards.

Alvaro.

[akazimli]

API 520 takes part of the choked orifice formula and builds it into a pseudo C factor. API further simplifies the C factor formula by hiding the gas constant in it as well as unit conversions. Unfortunately API saves pages by not showing the derivation of this pseudo C factor. These shortcuts can be convenient but they increase the chance that errors gets missed. The C factor formula SI units has a fixed multiplier of 0.03948. ( I found this at some forum and it makes clear part of the situation)

Regards,

Aydan

[MJG]

the conversion factors are inside the formulas

In this cases, using mathcad, you must to take out those factors from the formulas, and rewrite them in a better form.

That seems to be the case for the formulas Q = 70900*1*Awet and W = 3600*Q/λ.

So, maybe could get better help if you put some picture of the formulation that want to use in mathcad.

Putting aside all conversation regarding which variable notation and units are best, I think this comment from Alvaro is the key to OP's problem.  The number 70900 likely includes some unit conversion.  More information about the problem and/or equation would be helpful.

Additionally, please note that if you wish to use "W" as the built-in unit Watt, you probably should not also use it as a variable.

[akazimli]

Thank you all for comments, I changed speadsheet and it is works, but! I need A wetted in formula for Q in 0.82 power and when I make it units change again. What is the trick, please explain.

Regards,

Aydan

[Fred_Kohlhepp]

You've defined Q as two numbers without units times an area.

How do you expect it to be Watts?  For Q to be Watts, 70900 needs units:

of mass/(time cubed)

[akazimli]

Thank you all for comments, I changed speadsheet and it is works, but! I need A wetted in formula for Q in 0.82 power and when I make it units change again. What is the trick, please explain.

Regards,

Aydan

[akazimli · Accepted solution]

Thank you again! problem is solved!

Regards,

Aydan

[AlvaroDíaz]

Hi.

Check w, I guess it is wrong.

The way that you solve the problem, is one. The other is changing the formulation, for example, eliminate the factor 3600 as it is a convertion factor, but with this you loose the book formula. Another is using the API description, where they say in which units variables must to be expresed, and divede by them. In your case, Aw/m^2. And multipliying the result by the unit in which the variable description say that the final result was expressed, in this case watts. This method is, for me, better. With that, don't need to express the FC factor with those strange units. See the picture attached, from the page 108 of the pdf that I was posted above.

Best regards.

Alvaro.

[akazimli]

Hello,

thank you for answer.

I am confused, you made w unitles and then add required unit?

Regards,

Aydan

[AlvaroDíaz]

Hi Aydan.

Short answer is yes.

Long answer is: API, ASTM, ISO and a lot of "standards", carrying with them the private industry, are mathcad-less guys. They probably use excel or a hand calc to make their calculus. So, their equations usually needs that the "inputs" (variables in the right side of the equation) are expressed in some unit. In the W formula, Q must to be in watts, and L in J/kg. Then, the "output", W, goes to be expressed in kg/hr. 

When you use W = 3600*Q/L, as the book says, you goes direct to the trap: You expect that W goes to be expressed in the normal unit, kg/sec, but 3600 is a conversion factor. Thus, you must to make some work with units before have the correct answer.

Problem is that those standards usually uses a lot of empirical formulations, established by the "ancients", and there are no way to deduce or reinterpret them, thus, it could be a hard work to distinguish what is a conversion factor from a coefficient obtained by a lot of years of expertise operating dangerous and delicate equipment. That's the case for the 70,900 factor: which part is for convert units, and which other is a thermodynamic property for the fuel?

I'm not that radical as Stuart, who claim for a SWAT team, but some hours in a classroom with someone some few background about the practical and theoretical considerations for technical writing cold help, I hope. If not, call 911, it's ok.

Alvaro.