Tote capacity math calculation

Hello everyone

Real basic question, im currently working on a project that is simple to implement but i had some basic math questions to figure out.

This is an already existing application that works, im just making minor additions to it. All calculations are done in a cimplicity HMI as expressions however my question is basic enough that you don't need knowledge in cimplicity.

So here is my question.....

Their are Totes that have material in them. All the Totes are the same size, so the area and the capacity of how much material can be put in them is the same think of them as a rectangular cube. To measure how much material is in the tote, it is done with a 4-20ma pressure transducer in (psi). That 4-20ma signal comes into the HMI with a raw min value of 4000 and raw max value of 20000, which is scaled within the HMI to Engineering units of 0 to 12 (psi), so 4000 = 0 psi and 20000 = 12 psi, no scaling was done in the PLC. Currently the level reading is displayed in the HMI in lbs (pounds).

To get the level reading in lBS what they did was simply:

Value in (lbs) = (scaled pressure reading in psi)*(Area of the Tote)

so based on that all i'am trying to add as a display is the total capacity for the tote in units of (lbs) as the level reading is in pounds. In math to find the capacity of a rectangular cube, you just take the volume = length*Height*breadth and that is your capacity, however since i want to give the capacity value in lbs would the volume be correct??

Assuming the readout for the number of pounds for a tote is correct, simply fill one to capacity and let it be read. Keep the reading as your constant.

Yes, the variable you are missing is the density of the material. A pound of feathers would obviously require more room in the tote than a pound of bricks. The easiest way would be to just weigh a full tote as Bernie suggested (this assumes the density of your material is constant).

It's a pretty elegant way to get Lbs display.
lbs/in2 * in2 = lbs.

If you take the area * height.
in2 * in = in3 (cubic inches)

It's about 231 in3/gallon. That will give you the max capacity in volume. The max capacity in lbs, requires you to know the density.

If it's water (or close) a gallon weighs 8.34 lbs. If it's not water multiply the 8.34 lbs by the specific gravity to determine how many pounds/gallon.

It's all about the units.

EDIT: mellis beat me to the punch but you do still need to consider how compressible your material is, otherwise your density won't be constant.
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To convert the mass / weight in Lbs to volume you need a density of the material. Density is mass per unit of volume (say, lbs per sq ft).

So your equation would become:
weight / density = volume currently in tote.

As a side note, if you ever use SI units, mass is in Grams and weight/force is in Newtons, unlike in English/Standard units where a lb of mass is the same as a lb of force.

The issue with this is that depending on what material you are filling into the tote, the density of the material may change as it is compacted, especially if your material type is changing.

Assuming the tote is not under too much pressure, many liquids can be considered incompressible and the density can be assumed to remain constant (water, for example).

If you are filing with solid material or a rather compressible fluid/slurry, you density may increase as more material is added: the weight of the added material will compress whatever is already in the bag. In this case, if you used a constant density, your volume calculation may read a larger volume than actually exists in the tote.

It an actual volume feedback a "need to have" addition or are you just looking to show the current capacity level?

If the latter, it may be easier to measure the weight of the bag when it is completely full and then show the capacity as a percentage of the "full" weight.

This may need to change if you are filling with different materials.

Hope I did not over-analyze!

If you really need volume, you should consider investing in some type of level measurement device.

If you have the pressure at the bottom of the container and the uniform cross section area of the container then you have everything you need. You don't need to know density or specific gravity or bulk modulus or anything else.

Pressure is force or weight per unit of area. When a pressure is multiplied by an area then the area units cancel and you are left with units of force or weight.

Put another way, imagine your container is filled with little 1" x 1" columns of material. The weight of each of those little one inch square columns is by definition exactly equal to the pressure the column exerts on the bottom of the container in pounds per square inch. So all you need to do is multiply the weight of a 1x1 column (which equals the pressure) by the number of 1"x1" columns in the container. The number of 1x1 columns in the container is the area in in².

TConnolly said:

If you have the pressure at the bottom of the container and the uniform cross section area of the container then you have everything you need. You don't need to know density or specific gravity or anything else.

Click to expand...

This gives him weight, but not volume (or "level"). He needs density for this.

For example, if he is filling a tote with paper scraps, imagine the paper filling half-way up then collapsing in on itself and sinking into the tote. Even though there is more paper, it might be lower in the tote (and thus a lower volume).

All he wants is weight capacity of a full tote. Since pressure is being measured to obtain weight then I'm assuming this is a uniform material or liquid, or this existing system would not function correctly. Any material suitable for measuring this way will have a sufficiently high bulk modulus that at a mere 12 PSI compression is negligible. Fill at tote, measure the pressure, multiply by the area, and that is its weight capacity.

Thanks for the info guys, so luckily the operator gave me a list of all the raw materials in each and ever single tote which includes the density of the material in each Tote in lbs/gallon. So since i have the variable that was missing which is the density, the tote capacity will be computed as follows and correct me if im wrong:

Volume = length*breadth*heght = volume (in cubic inches), this is the max capacity in volume

so now to get it in pounds i first convert it to gallons as follows:

(in3)*(231gallons)/(in3), so now the inches cube cancel and you are left with a value in gallons.

So lastly to get the capacity knowing the density of material, as an example take water which has a density if 8lbs/gal we do as follows:

value in gallons *8lbs/gallons, so finally your gallons cancel out and your left with a value in pounds for the Tote capacity. Let me know if this is correct as i have to do this 30 Totes.


*Edit

Or as Tconnolly has stated i have the Psi reading, say for example im reading a Pressure reading of 12Psi at its max then :

(Current Pressure reading)*(cross sectional area) = max Capacity in Lbs

12lbs/in2*in2 = 12lbs so finally 12lbs is you max tote capacity in lbs.

*Second Edit

@ Tconnolly, wouldn't your suggestion give you the current fill level though as opposed to the capacity of the Tote, because say your pressure reads 6psi then the value in lbs for the max capacity would still read 6lbs?

There are 231 cubic inches per gallon. Therefore in your description of the conversion to gallons your expression should read 231in3/gallon instead of 231gallons/in3 and you should divide the tote volume in cubic inches by 231, not multiply as you showed.

@ steve thanks its been a long day going on 14hr and still going, anyways here is the edit....

Volume = length*breadth*heght = volume (in cubic inches), this is the max capacity in volume

so now to get it in pounds i first convert it to gallons as follows:

(in3)*(gallons)/(231in3), so now the inches cube cancel and you are left with a value in gallons.

So as an example say we calculated the volume to be 10cubic inches

10in3*1gallons/231in3 = 10/231 gallons;

So to get the Tote capacity of how much material it can hold assuming the material is water, which has a density of 8lbs/gallon it would be:

10/231gallons*8lbs/gallon = 10/231*8lbs = 0.34lbs

So 0.34lbs is the maximum amount of water that can be available in the tote. If this is still wrong then i need to sleep.

I usually try to do a sanity check on calculations like that. Substitute 231 cubic inches instead of 10 in your calculation. You come out with 8 pounds so you're good to go.

thanks steve now i have my total capacity in lbs equation, now its time to do this 30 times. thanks once again guys

@ Tconnolly you are indeed correct sir, you don't need density of the material or gravity to calculate your max tote capacity in lbs.

First way i did it was as others suggested getting your volume in inches cubed. That will be your total capacity in volume. To get the max capacity in lbs, I converted the inches cube volume reading to gallons then multiplied with the density of the material which also had units in lbs/gallons, so the gallons cancel and you are left with your max capacity in units of lbs.

Here is the problem with that. Assuming the density of the material stays the same, we can say that the max capacity in lbs will be constant. In my case my Psi readings were scaled from 0-12Psi, so when you want to calculate the current fill level its simply Pressure reading*area. But if say the Psi reading was at 12Psi max and you multiply that with your area, the final reading will be greater than your calculated max capacity.

Now if we simply calculate the max Psi reading being 12 psi and multiply it with area that will indeed be your max capacity that we need and as long as our 0-12Psi scaling is kept the same the current pressure reading will never exceed the max capacity.

So in conclusion as long as you have Pressure coming and you know the cross sectional area, that is all you need to calculate both the current and max readings in LBS.