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1. At time t = 0 a tank contains Q, Ib of salt dissolved in 100 gal of water. Assume that water containing 1/4 Ib of salt/gal is entering the tank at a rate of r gal/min, and that the well-stirred mixture is draining from the tank at the same rate. Set up the initial value problem that describes this flow

1. At time t = 0 a tank contains Q, Ib of salt dissolved in 100 gal of water. Assume that water containing 1/4 Ib of salt/gal is entering the tank at a rate of r gal/min, and that the well-stirred mixture is draining from the tank at the same rate. Set up the initial value problem that describes this flow

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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1. At time t = 0 a tank contains Qo Ib of salt dissolved in 100 gal of water. Assume that water containing 1/4 Ib of salt/gal is entering the tank at a rate of r gal/min, and that the well-stirred mixture is draining from the tank at the same rate. Set up the initial value problem that describes this flow process. Find the amount of salt Q(t) in the tank at any time, and also find the limiting amount QL that is present after a very long time. If r = 3 and Qo 2Q, find the time T after which the salt level is within 2% of Q. Also find the flow rate that is required if the value of T is not to exceed 45 min. %3D %3D
Transcribed Image Text:1. At time t = 0 a tank contains Qo Ib of salt dissolved in 100 gal of water. Assume that water containing 1/4 Ib of salt/gal is entering the tank at a rate of r gal/min, and that the well-stirred mixture is draining from the tank at the same rate. Set up the initial value problem that describes this flow process. Find the amount of salt Q(t) in the tank at any time, and also find the limiting amount QL that is present after a very long time. If r = 3 and Qo 2Q, find the time T after which the salt level is within 2% of Q. Also find the flow rate that is required if the value of T is not to exceed 45 min. %3D %3D
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