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 Post subject: Steam Table Values Derivation
PostPosted: Sun Jun 10, 2018 1:41 pm 
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Joined: Thu Nov 19, 2009 11:53 pm
Posts: 312
Location: Cheshire, UK
Boat Name: Frances Ann
Hi Folks

A question for the engineers amongst you.

I am messing about with some example calcs in the Steamboating Guide and trying to create a spreadsheet that could output answers to a wider range of inputs. I need to use Vg the Secific Volume of steam against pressure P. This is available in the tables, but rather than create a Lookup Table in the spreadsheet I would rather use the formula for that line. I can recall how to create a regression line from the data, but have forgotten how to derive the formula for a non linear line. I am sure it is available somewhere in a reference text but I cannot seem to find it.

Thanks

Pete


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 Post subject: Re: Steam Table Values Derivation
PostPosted: Mon Jun 11, 2018 1:43 am 
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Joined: Fri Nov 20, 2009 5:34 am
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Location: Phila PA USA
Boat Name: Margaret S.
The ASME steam tables are developed with much high-end mathematics, and all of the formulas are given within that publication, but in my view, far too complicated unless you need answers that are really accurate.

If you have access to EXCEL, there is a graphing feature, you plot several points of interest, then tell EXCEL to fit the curve, you can try polynominals, exponentials, etc. and usually a second or third order polynominal will be accurate enough. EXCEL will also display the formula iff you specify this feature.

When fitting thermodynamic properties I usually select a general equation form:

Y = A + B * ( X - Xo ) ^ Alpha

Playing with the constants you can usually arrive at a function that is better than the functions EXCEL is pre-programmed for, but it does take some time, fiddling with A, B, Xo, and Alpha. I usually write MACROs to step the constants up and down, it makes finding the right constants much faster. The "Goal Seek" feature in EXCEL also often works well, searching constants to make the least squares error becoming Zero.

For example, saturation temperature (F) as a function of saturation pressure (PSIA), in the vicinity of atmospheric pressure up to several hundred PSIA:

T = 117.17 * P ^ .22322

And a much more crude approximation of the saturation curve, yet doable with a $3 calculator, pressure is BarA, temperature is C:

P = ( T / 100 )^4

Just a little question: why is this post in "Non Engines and Boilers"?


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 Post subject: Re: Steam Table Values Derivation
PostPosted: Mon Jun 11, 2018 1:33 pm 
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Joined: Thu Nov 19, 2009 11:53 pm
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Location: Cheshire, UK
Boat Name: Frances Ann
Hi Fred

Many thanks indeed for that information. I will save that for future use.

As it happens I have done some revision for my spreadsheet formulae skills and ended up using a lookup table with data copied from the Steam Tables. Once I thought about what I was doing I only needed a dozen or so figures so it was not the chore I had originally expected.

Why post my question here? My thinking was that it is related to boilers, but it is not about physical boilers as such. I guess that it should really have gone into Anorak's Corner as it is not the sort of question that gets asked regularly.

Thanks again.

Regards

Pete


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