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Differential Equation  Brine Solution Entering Tank 
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#1
Feb2408, 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 wellstirred 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. 


#2
Feb2408, 08:48 PM

P: 1,635

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+(RiRo)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!! 


#3
Feb2408, 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.



#4
Feb2408, 09:13 PM

P: 1,635

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 wellstirred 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+(22)*t) dS/dt=42S/80, just solve this diff eq, if you haven't gone like this. 


#5
Feb2408, 09:19 PM

P: 1,635

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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