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J. Perelman
"Entertaining physics". Book 2.
Chapter 6. Properties of liquids and gases

THE PROBLEM OF THE POOL

From said one step to the notorious problems of the pool, without which no cost, no arithmetic and algebraic programming Taskbook. Everyone remembers the classic-boring, scholastic tasks like the following:

"In the pool held by two pipes. Through one of the first empty the pool can be filled in 5 hours; over one-half full pool can be emptied in 10 hours. In how many hours will be filled with empty the pool, if you open both tubes at once?"


The problem of the pool.

Tasks of this kind have respectable prescription - nearly 20 centuries, going back to " the Heron of Alexandria. Here is one of garanovich tasks - not so, however, elaborate on how the descendants of:

Four fountain given. Extensive given reservoir.
During the day, the first fountain fills it to the brim.
Two days and two nights, the second over the same should work.
The third is three times than the first, weaker.
In four days for him keeping up.
Answer me soon, whether he be full,
If during one all of them open?

Two thousand years solved the problem of pools and - such is the power of routine! two thousand years solved incorrectly. Why it's wrong - you will see that after what we had been told about the leakage of water. As you learn to solve problems about the pools? First, for example, are doing so. In 1 hour the first pipe pours 0,2 basin, the second pours 0,1 basin; hence, under the action of both pipes in the pool every hour arrives 0,2 - 0,1 = 0,1 where for the time of filling of the basin is obtained 10 hours. This reasoning is incorrect: if the flow into the water can be considered as taking place under constant pressure and, consequently, uniform, leakage occurs at varying levels and, therefore, is uneven. From the fact that the second pipe, the pool empties at 10 o'clock, does not mean that the hourly flows of 0.1 percentage of the pool; school admission decisions, as we can see, is wrong. To solve the problem correctly by means of elementary mathematics it is impossible, and therefore the task of the pool (flowing water) do not place in an arithmetic problems.

Entertaining physics J. Perelman

 




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