Differential Equation - Brine Solution Entering Tank


by Onett
Tags: brine, differential, entering, equation, solution, tank
Onett
Onett is offline
#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.
Phys.Org News Partner Science news on Phys.org
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)
sutupidmath
sutupidmath is offline
#2
Feb24-08, 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+(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
Onett is offline
#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
sutupidmath is offline
#4
Feb24-08, 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 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
sutupidmath is offline
#5
Feb24-08, 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!!!!


Register to reply

Related Discussions
Salt Tank - Differential Equation Calculus & Beyond Homework 3
Solution Of A Differential Equation] Calculus & Beyond Homework 7
Solution of a differential equation? Differential Equations 1
differential equation tank problem Differential Equations 5
Solution for the Differential Equation Differential Equations 2