ACCEPTED SOLUTION
Accepted Solutions
As Valery already pointed out that formula in your Appendix is not quite clean concerning units. The example given there is calculated dimensionless, as Valery has done.
I would correct the fact, that Ma2 has no unit by assigning the constant 3.23*10^(-5) the appropriate unit. I'm not sure about units of Z and esp. M !??
The reason you are not getting the answer you expect is, that qm and P2 are not using basic SI units. You may compensate by multiplying qm by 3600 (kg/s --> kg/hr) and dividing P2 through 1000 (Pa --> kPa). That way you have at a formula with a constant of 116.28 you may use with data of any units (as long as your worksheets units are set to SI units in preferences).
To get only the positive solution you would normally use the modifier "assume, d>0", but the symbolic engine does not know anything about units at all. Thats the reason you see kPa, m etc. in the symbolic result - the symbolic engine sees them as unknown variables. Because of that I had to use "assume, ALL>0" to make it work.
Hope it helps.
BTW, is there a specific reason you are appending the literal subscript point to the names of all variables which do not use subscripts ("Z." instead of "Z", etc.)?
Garrett,
A formula such as you have used has assumed a certain set of units, not always a set that is true to a standard such as SI. Therefore, the writeup should also define what units are to be used with each variable. So when the formula calls for a length, for example, in inches, you must supply the number of inches. If you have defined the length, L, with units, say SI units, then to get the length in the value of inches, you divide by the unit you wish, L/in. The result is now dimensionless (i.e. has no unit attached), and it is the correct number to use for the formula. This is the procedure that Valery used.
So to answer one of your questions, yes Mathcad converts everything to the base set of units that it has been told to use or to SI by default if you haven't switched the base units. Even though you may have defined the variable in the correct units for the formula, Mathcad converts it to the base unit. In the example I used above, L would be in m for SI set. If you put just L in the formula, the answer would not be correct.
Regarding the relative molecular mass, it appears that it really means the molecular weight of the gas, not a ratio of molecular weights to a standard gas. I say that because everything works fine if M is assigned a unit of gm/mol.
Formulas such as the one you are using were developed to make things easier for the user by combining conversion constants into one constant. I don't like them because as this example shows, they may have also used simplifying assumptions. When you see a formula such as this, it would be a good idea to check it with a more basic derivation such as the one I presented earlier. You will also understand the fundamental physics or engineering much better.
In the worksheet I provided earlier, I left out Z because it was 1. To be correct, the formula should be as shown below:
Garrett Ramjattan wrote:
I was using API-521 for flare sizing calculation and using the values they gave.
Send please this picture to authors of API 521Pressure Relieving and Depressuring
They authors are confused, and other confused!
Now for example we have not same problems in the The International Association for the Properties of Water and Steam (http://www.iapws.org/)
We publish not only a pdf document (formulations) but Mathcad sheet too
See please one example - http://www.iapws.org/relguide/ThCond.htm
As Valery already pointed out that formula in your Appendix is not quite clean concerning units. The example given there is calculated dimensionless, as Valery has done.
I would correct the fact, that Ma2 has no unit by assigning the constant 3.23*10^(-5) the appropriate unit. I'm not sure about units of Z and esp. M !??
The reason you are not getting the answer you expect is, that qm and P2 are not using basic SI units. You may compensate by multiplying qm by 3600 (kg/s --> kg/hr) and dividing P2 through 1000 (Pa --> kPa). That way you have at a formula with a constant of 116.28 you may use with data of any units (as long as your worksheets units are set to SI units in preferences).
To get only the positive solution you would normally use the modifier "assume, d>0", but the symbolic engine does not know anything about units at all. Thats the reason you see kPa, m etc. in the symbolic result - the symbolic engine sees them as unknown variables. Because of that I had to use "assume, ALL>0" to make it work.
Hope it helps.
BTW, is there a specific reason you are appending the literal subscript point to the names of all variables which do not use subscripts ("Z." instead of "Z", etc.)?
Do you know that Ma (Mach Number) and Z (compress. factor) are not dimensionless values!
In Mathcad MM and in Mathcad Prime Minister 
Ma + Z= error message. As Re + Nu = error message, e+pi = error message etc
Garrett Ramjattan wrote:
Thank you all.
and I believe the 22.4 is the value for volume at STP, of 22.4 m^3/kmole
You welcome!
22.4 is L/mole - one mole of an ideal gas need 22.4 liter - I remember it from school 
Garrett Ramjattan wrote:
Well both of you gave me correct answers...
One joke
Khwaja friend came to consult him about the case. He told him everything and at the end said, "Well? Am I wrong?" Hodge said: "You are right, my friend, you are right." The next day, who knew nothing about it as the enemy came to Hodge. And he also, wanting to determine what will end litigation, told him the case, of course, biased, in the light of its own advantage. "Well, Hodge, what would you say? Am I not right?" - He asked Hodja. And he Hodja answered, "Sure, sure, you're right."
Hodja's wife accidentally listened to his conversation with the litigants, and seeing that Khoja said both right, it planned to embarrass him and said: "Effendi, yesterday was at your neighbor Korkut, he explained to you the business, you tell him that he was right. Then came Sanjar his opponent, you and told him that he was right. How? Kazi you and I for so many years, his wife Kazi. Would be right at the same time and the plaintiff and the defendant? "Hodge said quietly, "Yes, it is, my wife, and you are also right.
