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Differential Equation - Brine Solution Entering Tank

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Onett
#1
Feb24-08, 08:36 PM
P: 2
1. The problem statement, all variables and given/known data

A tank contains 80 gallons of pure water. A brine solution with 2 lb/gal of salt enters at 2 gal/min, and the well-stirred mixture leaves at the same rate. Find (a) the amount of salt in the tank at any time and (b) the time at which the brine leaving will contain 1 lb/gal of salt.

2. Relevant equations

I'm just wondering about (b) really. I know we set S=80 below to solve it, but why?

3. The attempt at a solution

The differential equation that gives (a) is

S=160 - 160*e^(-t/40)

where S is the amount salt in the tank at any time t.
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sutupidmath
#2
Feb24-08, 08:48 PM
P: 1,633
If you correctly modeled a diff. eq for this problem and, also correctly solved it to come up with the sol

S=160 - 160*e^(-t/40), then part b)is not a problem at all. what it is asking u is that when will S(t)=1, and not 80 as you are saying!
remember S(t) is the amount of salt that the tank contains at any time.
The diff eq for this problem is

dS/dt=Ri*Ci- (S*Ro)/(Vo+(Ri-Ro)t) , where

S--- is the amount of salt in the tank,
Ri rate in
Ro rate out
Ci concentration in
Vo the initial volume

EDIT: You haven't actually showed us what u have done at all, remember one of the forums main policy is that you must first show your work, for after the people here to give you hints!!
Onett
#3
Feb24-08, 09:07 PM
P: 2
Oh, I'm sorry about that. I'll be sure to put up my work soon. Are you sure that what it's asking though? My notes say that I should get somewhere around 28 minutes.

sutupidmath
#4
Feb24-08, 09:13 PM
P: 1,633
Differential Equation - Brine Solution Entering Tank

A tank contains 80 gallons of pure water. A brine solution with 2 lb/gal of salt enters at 2 gal/min, and the well-stirred mixture leaves at the same rate. Find (a) the amount of salt in the tank at any time and (b) the time at which the brine leaving will contain 1 lb/gal of salt.

here it is :

dS/dt=2*2- (S*2)/(80+(2-2)*t)
dS/dt=4-2S/80, just solve this diff eq, if you haven't gone like this.
sutupidmath
#5
Feb24-08, 09:19 PM
P: 1,633
and for the part b) it is just asking you at what time t=? will S(t)=1, like i said.
NOTE: Next time show your work if you want to recieve any help!!!!


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