A system of two 3000 L holding tanks is set up with a pipe bringing water to the first tank, another pipe taking water from the first tank to the second, and a final pipe draining away from the second tank, with each pipe moving 100 L/hr. Usually, the system holds nothing but pure water, with the tanks kept half-full. One day (or so the story is told), an apprentice spilled a 60 kg bag of salt at the mouth of the pipe feeding into the first tank. To add further injury to the original injury, the bag itself flew from his grasp and partially clogged the pipe draining from the second tank (don’t ask how – it just did). If the pile of salt is being dissolved by the water at the rate of half of the remaining amount every ln 2/3 hours (if you don’t end up glad that this number is ugly, then you made an error) and if the drainage pipe now only carries 50 L/hr, what is the amount of salt in the second tank at the moment it fills up (and right before the pipes burst)? As usual, assume everything mixes instantly.
A system of two 3000 L holding tanks is set up with a pipe bringing water to the first tank, another pipe taking water from the first tank to the second, and a final pipe draining away from the second tank, with each pipe moving 100 L/hr. Usually, the system holds nothing but pure water, with the tanks kept half-full. One day (or so the story is told), an apprentice spilled a 60 kg bag of salt at the mouth of the pipe feeding into the first tank. To add further injury to the original injury, the bag itself flew from his grasp and partially clogged the pipe draining from the second tank (don’t ask how – it just did). If the pile of salt is being dissolved by the water at the rate of half of the remaining amount every ln 2/3 hours (if you don’t end up glad that this number is ugly, then you made an error) and if the drainage pipe now only carries 50 L/hr, what is the amount of salt in the second tank at the moment it fills up (and right before the pipes burst)? As usual, assume everything mixes instantly.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A system of two 3000 L holding tanks is set up with a pipe bringing water to the first tank, another
pipe taking water from the first tank to the second, and a final pipe draining away from the second
tank, with each pipe moving 100 L/hr. Usually, the system holds nothing but pure water, with
the tanks kept half-full. One day (or so the story is told), an apprentice spilled a 60 kg bag of salt
at the mouth of the pipe feeding into the first tank. To add further injury to the original injury,
the bag itself flew from his grasp and partially clogged the pipe draining from the second tank
(don’t ask how – it just did).
pipe taking water from the first tank to the second, and a final pipe draining away from the second
tank, with each pipe moving 100 L/hr. Usually, the system holds nothing but pure water, with
the tanks kept half-full. One day (or so the story is told), an apprentice spilled a 60 kg bag of salt
at the mouth of the pipe feeding into the first tank. To add further injury to the original injury,
the bag itself flew from his grasp and partially clogged the pipe draining from the second tank
(don’t ask how – it just did).
If the pile of salt is being dissolved by the water at the rate of half of the remaining amount every
ln 2/3 hours (if you don’t end up glad that this number is ugly, then you made an error) and if the
drainage pipe now only carries 50 L/hr, what is the amount of salt in the second tank at the
moment it fills up (and right before the pipes burst)? As usual, assume everything mixes instantly.
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