Making a Volume Measuring Stick

Hi,

I'm sure this formula is on the boards here somewhere, but thought I would post the formula for marking a stick to measure the volume of liquid in a round container as a function of the height of the liquid. So, here is how to figure out where to mark your dowel to indicate number of gallons:


Formula to Calculate Height Based on Volume is

h = v/pi r^2

Where h is height, v is volume, pi is 3.1415, and r^2 is radius squared

Note: radius = diameter/2
Note: 1 gallon = 231 cu inches

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Here is an example of how to solve for height in inches of a given volume, in a given pot diameter, say

4 gal. in 14" pot


h = v / (pi)(r^2)

h = 4*231/(3.1415)(7^2)

h = 924/(3.1415)(49)

h = 924/153.93

h = 6" for 4 gallons in 14" pot

all I did was pour a gallon of water in a pot then mark it... then poured two gallons then marked it ... 3. 4.. etc... I dont know about using a formula... but then again I forgot everything in learned in high school and college.

At first I thought this thread was funny because I thought it was somebody's sarcastic response then I realized it was 100% serious. That formula makes baby Jesus cry.

It better be one hell of a fancy stick...

Cheers

Take the largest accurate measuring cup you have and measure out a gallon in a pitcher or something. Mark the pitcher and then began filling the kettle from the pitcher. Ever addition mark or knotch a spoon or a spare plastic racking tube. The people at the brew store thought it was the neatest thing when I broke out the measuring stick.

Dilligans said:

all I did was pour a gallon of water in a pot then mark it... then poured two gallons then marked it ... 3. 4.. etc... I dont know about using a formula... but then again I forgot everything in learned in high school and college.

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This is what I did, too

Pouring in water is more accurate than measuring and calculating. With every measurement you introduce error. Also pots aren't always perfect cylinders. The error may be minimal, but when you can get it just about perfect with the volume method, why not? There's a time and place for calculation.

Example, you want to figure out the optimal place to put a floor drain. Do you shoot elevations and measure grade to find out where the low point is? No, you spray water on the ground and see where it collects. Easiest answer is usually the best.

When I first started brewing I set out to take the scientific approach to measuring my volume. The plan was to measure the height of the water with a nice stainless steel ruler and calculate the volume. Unfortunately, my pot has a bowed bottom and that wasn't going to work. So I fell back to pouring water in the pot in set volumes and marking a piece of pvc. The math is pretty but not always practical (and this from a physics degree carrying computer programmer).

GL using this formula in a Blichmann kettle...

Then again, it already has a calibrated sightglass, so I guess it doesn't matter.

There's a time for common sense/practicality and a time for science.
The smart individual knows when to use what, no matter which

Wow this degraded in an awful hurry....

Thanks for the formulas, that will be helpful in the future I am sure.

As to the comment regarding math introducing a bit of error with every calculation, we are marking these with a sharpie.. not exactly rocket science precision there. If you consider laser engraving this onto a stainless steel rod then you have the precision but then again you are going to have to compute where to put the marks.....

runing that calc one or twice... maybe. a bunch of times to lay out the whole stick - i have a headache just thinking about it.

has anyone developed a calculator that'll do the same thing?

I don't know about you guys, but I have a heating element, tubing for recirculating. Not to mention the pick up tube and big screen in my boil kettle.
It would be pretty difficult to calculate that displacement.

While we are on this topic, which do you guys think is more accurate.
Measuring the water by weight or using a measuring glass several times to fill to a gallon container?

Apoxbrew said:

runing that calc one or twice... maybe. a bunch of times to lay out the whole stick - i have a headache just thinking about it.

has anyone developed a calculator that'll do the same thing?

Click to expand...

Yeah, it's called Excel. Okay, I apologize for the tone I'm giving the board here but I just read the whole thread, from well intentioned formula post, followed by well intentioned measuring post, followed by string of misunderstanding and jump-to-conclusionsing. Now, my .02.

I tried measuring, and for me it didn't work out well. I have a nick in my stir spoon with which I have 5 gallons marked. I should really measure out 6.5 gallons (starting boil volume) and mark it, but I find it easier to just keep a measuring tape on hand. When draining my runnings I simply stick the tape in the wort, remember that number, and go to excel. Plug it into the formula and it gives me gallons. This is convenient for me because I also record my gravity, time to drain, etc. That and I like using excel and writing simple formulas. As an example I've attached a GoogleDocs spreadsheet of my most recent brew. https://docs.google.com/spreadsheet/ccc?key=0An-R1HUb1LH7dEhKME1fQjNPM0x6WVJIWktfUGNLRXc

Kyle

I agree that the bottom of kegs are curved and math needs to account for that or be inaccurate. It's faster to fill with water and mark. Very practical. Having said that mt turkey fryer is clearly marked one gallon but I estimate it's about 1.28 gallons. That's not a gallon! So I need to stress the "use an accurate measure" part. My initial gauge was off by gallons because I thought the fryer kettle read true. When my 15 gallon kettle "only" held about 12- I knew I had an issue.

I think the idea of precisely marking is all lost when you consider you cannot look straight on to counter the effect of the meniscus. With a really big diameter pot you could be liters off. We as brewers can afford some measuring error so might as well just employ the KISS principle.

Conan said:

Yeah, it's called Excel. Okay, I apologize for the tone I'm giving the board here but I just read the whole thread, from well intentioned formula post, followed by well intentioned measuring post, followed by string of misunderstanding and jump-to-conclusionsing. Now, my .02.

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easy pal... i wasn't trashing the OP in any way. i was making a silly comment about doing math. jumping to conclusions based on a post like mine isn't any better than trashing the OP for posting useful information.

here's a complete excel for anyone interested. all you have to do is punch in your diameter... so i've removed the need to do any calculations (even radius)!!

http://dl.dropbox.com/u/6060463/Volume_as_Height.xlsx

enjoy.

EDIT: by the way - the sheet i posted rounded all measurements to the nearest 16th of an inch since that's the standard on most peoples tape measures.

tmurph6 said:

Pouring in water is more accurate . . .

Click to expand...

For my 15 gallon I poured in the first gallon and marked the stick, poured in three more gallons and marked that. Took the average from the three gallon measurement and marked the rest of the stick in gallons. Because of the radius at the base of the pot and space taken by things like valves and false bottoms the first gallon has to be a direct measurement. After that the formula or taking an average of a larger sample will get you close enough.

updated with quart measurements too...

http://dl.dropbox.com/u/6060463/Volume_as_Height.xlsx

And what about figuring the expansion of a liquid when heated? Ugh, this brewing thing is becoming too darn complicated

(kidding).

Wow, I'm needing to mark my kettles or a stick, so I thought this would be an interesting thread. 4 pages, mostly of weird jabs or perceived jabs.

I think it's cool that rcole shared this formula. It can certainly be useful. So can pouring in water and marking the stick. There are issues with both. Surface tension or being less than perpendicular could throw off the pour-and-measure technique. A bowed kettle bottom or displacement by equipment could do a number on the formula. If a couple of ounces in a 15g batch throws off your recipe, you're probably doing something else wrong.

We're sharing information here. It's all good. Some people geek out on numbers, others on welding and grinding, others on developing software. RDWHAHB. Take in the info that helps, appreciate the passions of others, and ultimately you'll do it the way you want anyway. Just keep making (and drinking) beer.

I, for one, welcome our new beer brewing mathematician overlords I just looked this equation up the other day for my new boil pot. It just seemed easier than dumping 8 gallons of water!

zymolomancer said:

i, for one, welcome our new beer brewing mathematician overlords :d i just looked this equation up the other day for my new boil pot. It just seemed easier than dumping 8 gallons of water!

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+1

I like the math. Also, for a group of guys who are all hung up on numbers like OG, FG, brewhouse efficiency and on and on, it seems like you would welcome the formula. I'll be honest and admit that I made my sight glass by pouring from one calibrated vessel into another. Thanks mate!

Alright, what's the formula for dealing with a Sanke Keg shaped vessel?

Great, now what about the one with a fist sized dent in the bottom?

How about a large 50 gallon straight sided barrel that has a bottom that deflects in the center by about .25" at half full and .375" at full?

You can jack around with your slide rule all day while I get R dun with a weight-measured 5 gallon bucket ten times. I KNOW it's accurate.


The biggest problem with dipsticking for levels is that they don't work well in a tiered setup where the HLT is up above your head and they don't work well in the boil kettle, at least not in colder weather. It's hard to see the stick when you have to look through steam. It's probably less of a problem on smaller pots, but if there's a couple inches of headspace it's near impossible to see. I guess it can be made of wood so the level lasts a minute.

Many of the brewers' equipment (brewing equipment, that is) is dinged and not straight.

I calibrated my 1-gallon Cambro pitcher with 3.789kg (3.789kg of water = 3.789L of water = 1 gallon of water) of room temperature (20C) water. And then I started pouring the calibrated 1-gallon in the kettle and marking each gallon.

M_C

Don't need to stick it in the water/wort. Just at the surface, and have your markings read at the lip of the keg/pot. That being said, I have cylindrical 25G pots that are 50cm deep. I use a ruler.

I agree with KISS.

However, if you're going to be anal and insist on doing it mathematically, at least do it somewhat correctly with THIS *amazing* mathematical formula that any middle school student should be able to figure out on their own:

h = V/(πr² - l×w)

Thumbs up to the first person who can tell me why this one is better

emjay said:

I agree with KISS.

However, if you're going to be anal and insist on doing it mathematically, at least do it somewhat correctly with THIS *amazing* mathematical formula that any middle school student should be able to figure out on their own:

h = V/(πr² - l×w)

Thumbs up to the first person who can tell me why this one is better

Click to expand...

Accounts for added volume of measuring stick. Should be changed based on the shape of measuring stick (i.e. ruler vs. rod).

amb1935 said:

Accounts for added volume of measuring stick. Should be changed based on the shape of measuring stick (i.e. ruler vs. rod).

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Yeah, I thought of that, but I figured most "rods" would really be spoons that would be a fair bit more difficult

Of course, for a perfectly cylindrical rod, you can just replace l×w with πs² (s being the radius of the rod)

By shear coincidence, my brew pot is 36cm diameter, which handily results in 1cm=1 liter. A flat stainless metric rule makes life easy.

birvine said:

All I can say is 'wow'.

But I'll add more... what if the measuring rod is made of wood and absorbs some water. Now what? Chaos?

And finally, if said rod still floats does that make it a witch?

B

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If the rod absorbs water, it will take it all with it when pulled out, making it completely irrelevant

emjay said:

If the rod absorbs water, it will take it all with it when pulled out, making it completely irrelevant

Click to expand...

Make sure to add that volume back to the wort to keep things balanced.

B

EDIT: Tongue-in-cheek, by the way. I'm enjoying this measurement discussion roller coaster. LOL.

I use a piece of flat aluminum bar/strap I found at home depot. I did the pour & mark routine because my kettle is not a perfect cylinder. I then took a dremel tool and ground the marks and numbers into the metal. I wrapped the 'grabby' part with gaffers tape and it seems to work well. I know it isn't the most accurate thing, and the steam makes it hard to read in the dark, but I get close enough.

I am sure there are people out there who dont even measure their wort volume. I sometimes wish I could be like them.....

I found this very helpful, thanks OP. Bookmarked.

Conan said:

I should really measure out 6.5 gallons (starting boil volume) and mark it

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This was the most useful part of the thread for me---I can never figure out how much water to start with, in order to end with 5 gal after I add ingredients and boil for an hr, then drain through the spigot.

NewBrewB said:

This was the most useful part of the thread for me---I can never figure out how much water to start with, in order to end with 5 gal after I add ingredients and boil for an hr, then drain through the spigot.

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Depends on your rig. The 6.5 gal starting volume is sort of a rule of thumb. It typically assumes a 60 minute boil with 1 gal per hour boil off rate. Then it assumes you are siphoning your your wort from the kettle to the primary and leaving .5 gal of break material in the kettle.

I've been watching for a couple days now and I love it. I've. One up with a way to bring some facts to it but I'm away from my house for a while so I'm hoping someone will take over for me and report the findings. Or I'll just do it when I get back home.
Step 1: Do the pour and mark method and time yourself from start to finish.
Step 2: Do the math and measure method, timing yourself from start to finish.
Step 3: Do a little research and find out what a gallon of water weighs.
Step 4: Fill your pot with water a gallon at a time using one of the dip sticks as a guide while weighing it at each gallon interval.
Step 5: repeat with the other dip stick.
Now here's the part we all want to know.
Which method took the longest to complete?
Which one was the most accurate and by how much?
To be fair don't use your converted keg, we all know math won't work there. But, don't worry about if the pot has dents in it and if the bottom is warped, any cooking pot with a general cylindrical shape will do.
I'd do this myself but I'm away from my kitchen and would love to see results before I return / loose interest.
Oh by the way, I am an engineer and my prediction is that the pour and mark method takes grossly more time but they will be neck-n-neck on accuracy.

sdillow said:

And what about figuring the expansion of a liquid when heated? Ugh, this brewing thing is becoming too darn complicated

(kidding).

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Did this get addressed? This is a major point.

tektonjp said:

Did this get addressed? This is a major point.

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just checked that water is about 4% less dense at boiling. hmmm. RDWHAHB