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; nいw 8 24 dt water. How much sulr ir n MP The are nepo noreuah mred, and Jke water Plown fann

; nいw 8 24 dt water. How much sulr ir n MP The are nepo noreuah mred, and Jke water Plown fann

Advanced Engineering Mathematics
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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Question

differential equations

### Problem Statement A tank has pure water flowing into it at 12 L/min. The contents of the tank are kept thoroughly mixed, and the outflow also occurs at 12 L/min. Initially, the tank contains 70 kg of salt in 1000 L of water. How much salt is in the tank after 30 minutes? ### Explanation This problem involves a tank being filled and emptied simultaneously, maintaining a constant volume of water. The initial amount of salt is given, and the rate of water flow (in and out) is constant. The task is to determine the amount of salt remaining after a set duration, considering the continuous mixing. This is a classic "mixing problem" in engineering or chemistry, often solved using differential equations or integration.
Transcribed Image Text:### Problem Statement A tank has pure water flowing into it at 12 L/min. The contents of the tank are kept thoroughly mixed, and the outflow also occurs at 12 L/min. Initially, the tank contains 70 kg of salt in 1000 L of water. How much salt is in the tank after 30 minutes? ### Explanation This problem involves a tank being filled and emptied simultaneously, maintaining a constant volume of water. The initial amount of salt is given, and the rate of water flow (in and out) is constant. The task is to determine the amount of salt remaining after a set duration, considering the continuous mixing. This is a classic "mixing problem" in engineering or chemistry, often solved using differential equations or integration.
Expert Solution
Step 1

Given that:

  • Rate at which pure water flows into the tank = 12 L/min
  • Rate at which the content flows out the tank = 10 L/min
  • Initially, tank contains 10 kg of salt in 100 L of water

To calculate the amount of salt in the tank after 30 minutes.

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