Hornby Water Tank Problem

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From Walmart's website, I've gathered that the dimensions of an actual can of Campbell's condensed tomato soup is roughly r = 2.69in, h = 4.06 in. https://www.walmart.com/ip/Campbell-s-Condensed-Tomato-Soup-10-75-oz-Can/10321636

Most importantly, the ratio of heigh to radius is therefore: h/r = 1.51

Given that the Hornby Island water tank mentioned in the problem has the same proportions as a Campbell's soup can as described above, we can use the above ratio to determine an estimate for the height of the cylindrical tank after using an estimated height of the bike to estimate it's radius. 

The bike in the photo does not look to be sized well with the saddle too low relative to the handlebars, so researching typical saddle or handlebar to ground height may not produce an effective estimate. A ballpark estimate could be obtained from the wheel diameter though as almost all hybrid bikes (as pictured) use 26" wheel diameter.

Then, using Google Drawings, I was able to estimate the radius of the tank (at least get a lower bound on it, because of foreground-background effects on apparent length) as about 3x the wheel diameter. Therefore, 

r_tank = 3*26" = 78" = 1.981 m (approx)

Applying the ratio from earlier gives 

h_tank = 1.51*(1.981 m) = 2.99 m

Thus, an estimate for the volume of this water tank (assuming it is a perfect cylinder) would be

V_tank = pi*(1.981 m)^2*(2.99 m) = 36.86 m^3 = 36860 L

To figure out whether or not this volume of water would be sufficient to put out an average house fire, one would probably need to look at the average response time statistics for the local fire department, the average square footage of a house in that region, and the rate at which the water could be applied to the fire. This is well beyond what I'm prepared to do for a blog post that's overdue, but I hope somebody made these calculations when they designed the tanks. Google wasn't much help in sourcing a non-meaningful average amount water used for the "average" house fire either.

Extension

A possible extension would be to ask students to calculate the capacity of the basket on the bicycle, given a volume for the cylindrical water tank.




Comments

  1. Susan Gerofsky1 January 2021 at 14:39

    Good work, with the research, estimation and consideration of what would be needed to calculate the volume of water to put out a fire! I like your extension too, working from large to small.

    ReplyDelete

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