Horizontal Round Cylinder Tank Volume Formula

[Palm Beacher]

Hi All,

It probably has been discussed before....but...

My PLC is a AB L71 Processor (RSLogix5000 v20)

I have a Horizontal Round Cylinder Tank with Flat Ends.
I know the Length (864") and Diameter (94") and Radius (47") of the tank, and I have a
level transmitter to give me the height of the liquid inside in inches.

What formula do I use in my PLC to calculate the Volume inside
the tank.??

Thanks for your help,
Palm Beacher

 

[Dirt]

 

[Steve Bailey]

It is a complicated formula which you can easily find using Google. However, it requires a PLC with inverse trig functions in its instruction set. Lacking that, most implementations calculate the volume at different depths and use those values as breakpoints for a lookup table, with linear interpolation for depths between the breakpoints.

 

[Palm Beacher]

I wanted to use a CPT instruction to do this.

 

[Tom Jenkins]

The attached spreadsheet includes an empirical formula that give the volume as a fraction of the total volume. It can be executed on any PLC with four function math.

 

[Dirt]

The attached spreadsheet includes an empirical formula that give the volume as a fraction of the total volume. It can be executed on any PLC with four function math.

That's great! Thank you!

I was kind of bored, so I had to try and calculate the deviation between this and the more "advanced" formula in an ABB AC800M. Maximum deviation I got between formulas was only 0.6 percentage points [abs]. And then I'm not sure how accurate the "advanced" formula in that controller actually is..

 

[daba]

To be honest, given the lack of detail provided, your post looks like a homework assignment.

But here goes anyway...

Whilst the maths may require inverse trig functions, none of the formulae are that complicated for a simple cylinder with flat ends.

But I have to make the point that working from the stated (or even measured) tank dimensions is not going to give the best accuracy. Very rarely are tanks perfectly "cylindrical", very rarely are they the diameters specified on the design drawings, and things do get massively complicated with dished ends, tilted tanks, conical bottoms, and "inclusions" such as mixer paddles, heat-exchanger coils etc.

In your case you haven't specified whether your tank is tilted, most are, and where the height transducer is located (which does make a difference if the tank is tilted).

If accuracy is important (critical in some industries), then there are 2 methods which can produce accurate results.

1. mount the vessel on load cells, and use the weight to determine the volume. The PLC simply has to determine volume dependent on the density of the contents. Of course this is only applicable to contents that have a constant density (weight per volume).

2. produce a "dip-table" by filling through a certified flowmeter, recording the liquid height at predetermined intervals. This method is independent of the density of the product. Concentrate more readings where the height changes most rapidly versus height. The PLC can then interpolate between the "above" and "below" readings using a look-up algorithm. The more readings (intervals) in the dip readings, the more accurate the final result.

 

[Palm Beacher]

Since my last days of schooling was 43 years ago sonny...
I don't know why you think everything is a "homework" assignment.
Just trying to get my tank reading correctly.
See attached CPT

 

[mk42]

Since my last days of schooling was 43 years ago sonny...
I don't know why you think everything is a "homework" assignment.
Just trying to get my tank reading correctly.
See attached CPT

Often, when someone has a very low post count and their first post is a math problem, it's a student looking for someone to do their homework for them (usually with little effort on their part). We try to encourage them to learn for themselves. It isn't necessarily a judgment, probably at least partially a warning to the rest of us helpful folks to give you lots of useful info but maybe not the whole answer in one go.

 

[Tom Jenkins]

That's great! Thank you!

I was kind of bored, so I had to try and calculate the deviation between this and the more "advanced" formula in an ABB AC800M. Maximum deviation I got between formulas was only 0.6 percentage points [abs]. And then I'm not sure how accurate the "advanced" formula in that controller actually is..

The level transmitter probably isn't better than +/- 0.6% accurate. And there are the potential errors that daba pointed out.

However, there are two techniques you can use if you need more accuracy. First, open the spreadsheet. You can right click on the formula shown on the graph and increase the order of the polynomial from 3 to 4 or 5 or .....

If you double click on the formula and go to the number parameter you can increase the decimal places to whatever suits your fancy.

 

[Dirt]

The level transmitter probably isn't better than +/- 0.6% accurate. And there are the potential errors that daba pointed out.

However, there are two techniques you can use if you need more accuracy. First, open the spreadsheet. You can right click on the formula shown on the graph and increase the order of the polynomial from 3 to 4 or 5 or .....

If you double click on the formula and go to the number parameter you can increase the decimal places to whatever suits your fancy.

Yeah, if I'd ever need more accuracy then that I'd go the way daba describes with either known volume and a piecewise linear function or load cell.

If you use a higher polynomial order, you also have to consider higher order oscillation effects. But I guess this is just theoretical, which is fun from time to time.

 

[RonJohn]

While I haven't used it myself, I recently came across a Tank Volume AOI in the Rockwell Sample Code Search page by searching for the word "tank". Maybe this'll help someone down the road.

 

[BTL5]

While I haven't used it myself, I recently came across a Tank Volume AOI in the Rockwell Sample Code Search page by searching for the word "tank". Maybe this'll help someone down the road.

Thanks! This works great!

 

[drbitboy]

Thanks! This works great!

https://ntrs.nasa.gov/api/citations/19720010958/downloads/19720010958.pdf




For arccos, a two-term polynomial will get yield almost five digits (.001%), and three terms gets you all 23 bits of mantissa of a 32-bit real.

 

[Peter Nachtwey]

https://ntrs.nasa.gov/api/citations/19720010958/downloads/19720010958.pdf

For arccos, a two-term polynomial will get yield almost five digits (.001%), and three terms gets you all 23 bits of mantissa of a 32-bit real.

This is gold for the embedded programmer.