Additional Math Pages & Resources

Friday, June 4, 2010

Slow as what?

Today's we look at the concept of speed. Or the lack of it. I overheard Darcie in our office say, "That copier is as slow as molasses."

How slow is molasses? What is it anyway, and where did that saying come from?

Molasses is a syrup formed as a byproduct when sugar cane is turned into crystalline sugar. Different forms of molasses can be created from beet sugar, pomegranates, dates, etc. Basically it's a thick, gooey substance left behind when the sugars are removed from a juice or nectar.

But we want to know how fast molasses travels. In these two pictures, it seems to be pouring pretty slowly, doesn't it?

I found a story about the Great Boston Molasses Disaster where it was said that 2 million gallons of molasses exploded out of a large tank and flooded down the streets at an "estimated" speed of 35 mph. An interesting story but I think we can ignore it as a precedent for measuring speed of molasses. If you want to read more, there's a $10 book about it available on Amazon, called Dark Tide.

Let's stick to the facts though! Here's a comparison of the viscosity (gooey-ness) of several liquids, measured in units called centipose. All of these are at a temperature of 70 degrees F. The scale is based on the pour-ability of water:

0001      Water
0150      Maple Syrup
2000      Honey
10,000    Molasses
20,000    Hershey chocolate syrup
50,000    Mustard
150,000   Peanut butter
1,000,000 Lard or Crisco shortening

With this comparison we can see that molasses is pretty thick. It's much slower to pour than honey but not as slow as chocolate ice cream topping. And we can see that the mustard, peanut butter and lard aren't really what we would call liquids, or pourable. Maybe squirtable, in the case of mustard.

If you want to go into it further, here's a summary of a $40 research paper that you can buy, but it will probably read more slowly than molasses will pour in January!

The rheological properties of molasses were studied using a rotational viscometer at various temperatures (45–60 °C), with different amounts of added ethanol per 100 g of molasses (1–5%) and rotational speeds  (4.8-60 rpm). Flow behavior index of less than one confirmed that molasses has pseudoplasticity (n=0.756–0.970). 
  • The consistency coefficient decreased with the amounts of added ethanol, while the flow behavior index increased. 
  • The consistency coefficient decreased with temperature but no harmonious variation was observed in the flow behavior index values with increase in temperature. 
  • The apparent viscosity decreased with increasing temperature and shear rate, implying that molasses with or without added ethanol behaved as shear thinning. 
Mathematical models were developed for determining the apparent viscosity of molasses as affected by temperature and added ethanol. The suitability of the apparent viscosity models were judged by using various statistical parameters such as the mean percentage error, the mean bias error, the root mean square error, the modelling efficiency and chi-square.

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