How can I calculate the weight of chocolate in a tank without a scale?

[bkweibley]

First off Id like to say hello and I am glad I found this forum. Reading threw some of the threads, it sounds like we have a great group of people here.

I am trying to come up with a way to calculate the amount of chocolate being held in the chocolate reserve tank at my place of employment. Since we do not have a scale on this tank, my goal is to be able to take a measurement from the inside top of the tank to the top of the chocolate and be able to tell how many pounds we have left in the tank with that measurement.

I will be sharing this with others in my workplace also, so I will be placing it in a spreadsheet so that it is easy for everyone to use. The tank has straight sides, but a rounded bottom. The straight sides were pretty easy for me to figure out, but once the chocolate is down farther than 63" (where the slope starts) I am having a hard time grasping a way to come up with a formula for that part of the tank.

Being that I am using an excel spreadsheet with VBA I don't need one big formula, everything can be split up into smaller formulas that will perform behind the scenes in the spreadsheet.

The things that I do know are that a gallon of chocolate weighs 11.0995 lbs, and the bottom area that I am trying to figure out has a measurement from the top view of 192" x 90". From a side view of the tank(Small side 90") the tank appears to be a half circle with a 45" radius. That area of the tank holds 2,644 gallons or 29,347.078 pounds.

The overall depth of the tank, at the center is 108". The bottom 45" is what I cannot figure out. Here are some images that may help.

 

[mfb]

I think circular segment at wikipedia has the formulas you need.

 

[bkweibley]

I think circular segment at wikipedia has the formulas you need.

I was looking into circular segments, but it looks like circular segments refer to circles, not actual 3d objects? Doesnt look like the actual depth is taken into account?

That does look close to what I am looking for though. The green area would represent the chocolate in the bottom of the tank once we got into the bottom of the tank. If that does take the depth into account it would give me what I need. Honestly the equations are a little above my head though. I worked with sign and cosign and all of that stuff in trig class junior year in high school, but that was back in 2003... LoL

 

[SteamKing]

What you are looking for is called an 'ullage table'. It looks like you have the key tank dimensions to create this table. BTW, 'ullage' is the distance between the top of the tank and the surface of the liquid inside the tank.

It's relatively easy to calculate the gross volume of the tank. However, it looks like there is an agitator or stirrer which is mounted inside the tank. I would assume that no chocolate would be inside the pipe which serves as the axis for this mechanism. What is the outside diameter of the pipe? That would help give a more accurate table.

 

[bkweibley]

What you are looking for is called an 'ullage table'. It looks like you have the key tank dimensions to create this table. BTW, 'ullage' is the distance between the top of the tank and the surface of the liquid inside the tank.

It's relatively easy to calculate the gross volume of the tank. However, it looks like there is an agitator or stirrer which is mounted inside the tank. I would assume that no chocolate would be inside the pipe which serves as the axis for this mechanism. What is the outside diameter of the pipe? That would help give a more accurate table.

I don't have any information on the stirrer, although looking at the gallon sizes listed on the one image, I am assuming that they are taking the stirrer into consideration when giving those numbers?

If you look at the second drawing, the top 63" was pretty easy for me to figure out, because it tells me that on the flat walls, there are 74.8 gallons per inch. So that was just a matter of multiplying 74.8 by how much a gallon of chocolate weighs (11.0995 lbs) and then multiplying it by the number of inches the chocolate is from the top, to get how much chocolate is out of the tank. I also see that the bottom 45 inches of the tank holds a total of 2,644 gallons.

total gallons = 2,644 * (74.8*63)
total gallons = 7,356.4
total weight = weight of gallon of chocolate * total gallons
total weight = 81,652.361 lbs

If the measurement down to the top of the chocolate is 63 inches or less it would be pretty simple for me then.

amount in tank = 81,652.361 - [(74.8*11.0995)*inches]

if the measurement is more than 63" than Id subtract 63" from the total inches and then figure out how much of the 2644 gallons is missing from the half cylander at the bottom. This is where I am having problems figuring it out though. Is there a formula or series of formulas that I could use to figure this out, or is it not that easy?

 

[SteamKing]

Please find attached a spreadsheet I put together which calculates the values for an Ullage Table for the chocolate tank. Based on the capacity information included with the tank diagrams, that figure includes the volume of the stirrer. It appears that the stirrer is constructed using an 8" pipe, and the volume of this pipe totally submerged is approx. 50 gals.

The table can be printed by selecting the 'Ullage' tab and printing that sheet. The 'Calc' tab is the calculation for the tank capacity and the weight of chocolate.

 

[mfb]

I was looking into circular segments, but it looks like circular segments refer to circles, not actual 3d objects? Doesnt look like the actual depth is taken into account?

That does look close to what I am looking for though. The green area would represent the chocolate in the bottom of the tank once we got into the bottom of the tank. If that does take the depth into account it would give me what I need. Honestly the equations are a little above my head though. I worked with sign and cosign and all of that stuff in trig class junior year in high school, but that was back in 2003... LoL

The interesting quantity is the area at the surface, the volume is then just the surface area (as seen from the front) multiplied by the constant "depth" of the tank (186''?). And the formula for the surface area is given there.

 

[bkweibley]

Please find attached a spreadsheet I put together which calculates the values for an Ullage Table for the chocolate tank. Based on the capacity information included with the tank diagrams, that figure includes the volume of the stirrer. It appears that the stirrer is constructed using an 8" pipe, and the volume of this pipe totally submerged is approx. 50 gals.

The table can be printed by selecting the 'Ullage' tab and printing that sheet. The 'Calc' tab is the calculation for the tank capacity and the weight of chocolate.

This is an awesome spreadsheet SteamKing, thank you very much!