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Vendredi, 18 Novembre 2011 14:32

## How Many Sips in a Bottle of Beer?

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This is what I noticed about my beer glass after taking a few sips. WARNING: Since there is a beer in this post, I will have to ask to see your ID.

If it wasn’t a picture about beer, it could make a great WCYDWT (What Can You Do With This?). But those WCYDWT this problems seem to mostly be aimed at High School students. So, instead I will just analyze this myself.

What makes this glass so cool is that it looks like I drank each time from the same side of the glass. This means that the other side left a little beer head ring. What can I do? How about I estimate the volume of each sip?

On to Tracker Video (it is good for images as well as videos). Here is a plot of the height of the different rings on the glass.

A quick note. Tracker Video likes to pretend like each new data point in the picture is a new frame in the video. The time axis really should be “ring number” or something.

But what can I determine from this plot? Well, it seems like the height between the rings is pretty consistent. If this is indeed due to one sip of beer, then each sip is about the same size (since the glass has straight sides). What about the size of this sip? The length scale in this picture is based on height of the glass. So, the slope of the line above is -0.07 glasses per sip. But how big is the glass?

If the height of the glass is 1 (I will call this units gh for glass height). Using Tracker, I find that the diameter of the glass is 0.443 gh. Also, the top ring is at 0.721 gh. In terms of units of gh, the volume of the beer (all the beer) would be the same as the volume of a cylinder:

Since it is a beer, I know the volume. It should be 12 oz or 2.5 x 10-4 m3. I can use this to find the height of the glass.

I think 14.7 cm is a bit short for that glass. Maybe I am missing the top beer ring – or maybe this value is ok. At least it seems to be near to ok.

So, how about this? If each one of those rings is a sip, then how many sips are there in the bottle of beer? Let me write the linear function in the graph as:

Where n is the “sip number” in units of sips. Now, the question becomes: what sip number until the height (h) is at zero gh?

So, 10 sips of beer – at least for my sized sips. Not too bad. At least the next time someone asks for a sip of my beer (Eric, I am talking to you) I will know that I will have about 10% less beer afterwards.

One last note: I know what you are thinking. Why didn’t I just take a sip of beer and then spit it out into a measuring cup. I will tell you why not: because it’s beer. You just don’t do that with beer.

I guess I should do “how many licks are in a tootsie roll lollipop” next.

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