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The Gas Storage Tanks

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Stratgey 1 Problem Set 1








[pic 1]

34296 - Mona Strachota

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Exercise 1:

Jane Practice, a former student of 2422. Strategy 1, stated the following: “Elephants have harder time dissipating heat than small animals. In addition to differences in their physiology, this is also a consequence of the cube-square rule.”Please comment in no more than 10 lines, while agreeing or disagreeing.

ANSWER

We agree with Jane Practice!

The cube-square rule states that as a shape grows in size, its volume grows faster than its surface area. The rule indicates that the surface area is proportional to the square of the multiplier and its new volume is proportional to the cube of the multiplier.This fact helps explaining why large animals like elephants have harder time dissipating heat than small animals. The surface area an animal uses to dissipate the heat does not grow as fast as its body volume.

Exercise 2:

(i) How many gas storage tanks would you expect to find In a small town? [Note: the surface area of a sphere, A, equals 4r², whereas its volume, V, equals 4/3 r³; recall that r stands for the radius of the circumference.]

ANSWER

The gas storage tanks refer to the cube square rule. This rule is considered being one source of economies of scale. The increase in surface area is less compared to the increase in volume (capacity).

  • production capacity is proportional to volume
  • total cost of producing at capacity is proportional to surface area

The cost of pumping gas through a pipeline is proportional to its circumference and the distance travelled. By contrast, the amount of gas that can be pumped depends on the pipeline’s volume.

As an example, take r=1:

Surface Area (A):4 𝝿r² = 4 𝝿[pic 2]

Volume (V): 4/3 𝝿r³= 4/3* 𝝿*1³=4/3𝝿

[pic 3]

Now let´s assume r=2:

(A)=4𝝿 *2²=16𝝿

(V)=4/3*𝝿*2³=32/3𝝿

The cube square rule applies whenever output is proportional to the volume of the production vessels and costs are proportional to the surface area of the vessel. Saying this, when we double the size of a gas tank, the cost of the materials to make it (stainless steel/Surface Area) increases fourfold whereas the volume increases even eightfold.  

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