MTH 256 Lecture 10: 01302019

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taupealpaca220

10 Feb 2019

School

Oregon State University

Department

Mathematics

Course

MTH 256

Professor

T. Hatase

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Document Summary

A tank of maximum capacity 1000 gallons initially contains 10 lb of salt dissolved in 500 gallons of water. Brine that contains 0:5 lb of salt per gallon is pumped into the tank at 10 gallons per minute and at the same time water is drained from the tank at 5 gallons per minute. Assume the tank is always kept uniformly mixed. Calculate the amount of salt in the tank the moment it begins to over ow. amount of salt in the tank in lb . in lblmin for: et e 100. 1000 gallons . water coming in at out going qq. tn/=-8eb. 5 gall min . liquid tank amount the the of at in is 5001-5-1 gallons . t at time. 10 gallons per minute off: q=dat overflow or emptying qloflolb. 1- loot t q=5 amount liquid of changer salt: of "t. If an object of temperature t (t) at time t is in a medium of temperature.

Related Questions

Three Brine Tanks: There are three tanks. Initially the rst tankhas 500 gallons of brine

containing twenty pounds of salt, the second tank contains 200gallons of pure water, and

the third tank contains 1000 gallons of brine containing tenpounds of salt. Brine with a

concentration of 1 lb/gal is poured into the rst tank from anoutside source at a rate of

twenty gallons a second. There are also three tubes connectingthe tanks and they allow

fluids to pass as follows: brine is allowed to move from the rsttank to the second tank

through a tube that allows forty gallons a second to passthrough it, brine is allowed to move

from the second tank to the third tank through a tube thatallows forty gallons a second to

pass through it, and brine is allowed to move from the thirdtank to the rst tank through a

tube that allows twenty gallons a second to pass through it.Lastly, twenty gallons a second

are drained from the third tank and removed from the system.Assume salt is uniformly

distributed within each tank due to stirring.

1. First draw a picture of this situation.

2. Create a model that describes the amount of salt in eachtank at time t.

3. Solve the model. You will need to look at section 5.6 tolearn how to deal with a

nonhomogeneous linear system.

4. Plot your solutions on the same graph (you should havethree equations that you plot

against time t).

5. When does the concentration of the salt in the second tankreach 0:5 pounds a gallon?

6. What quantity of salt will each tank be nearing as t getslarge? How could we have

known this without even building a model?

MTH 256 Lecture 10: 01302019

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