Differential Equation mixing problem

Click For Summary

Homework Help Overview

The problem involves a differential equation related to a mixing scenario in a vat containing beer with varying alcohol percentages. The original poster describes a situation where a vat with 500 gallons of beer at 4% alcohol is mixed with beer at 6% alcohol, and they are trying to determine the percentage of alcohol after one hour.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to set up a differential equation to model the inflow and outflow of alcohol in the vat. Some participants question the use of the initial condition of 4% alcohol and its significance in the solution process. Others suggest clarifying the steps taken in solving the equation and checking the calculations involved.

Discussion Status

Participants are actively discussing the setup of the differential equation and the implications of the initial conditions. There is an ongoing exploration of the mathematical steps involved, with some guidance offered on how to manipulate the equation. However, there is no explicit consensus on the correctness of the approach or the final outcome.

Contextual Notes

There is a focus on ensuring that the initial condition is appropriately incorporated into the solution process. The discussion reflects uncertainty regarding the application of the initial percentage of alcohol and its impact on the results.

jordan123
Messages
15
Reaction score
0
Differential Equation mixing problem!

Homework Statement


A vat with 500 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 5 gal/min and the mixture is pumped out at the same rate. What is the percentage of alcohol after an hour?

The Attempt at a Solution



This is what I've been doing.

dA/dt = inflow - out flow
= (.06)(5) - (A/500)(5)
= .3 - (A/100)
= (30 - A)/100

etc but I feel I must be setting it up wrong or something ?? But it never gets the correct answer which is.

4.9%

If anyone can point out what's up that would be much appreciated!
 
Physics news on Phys.org


Your solution never uses the "4% alcohol (by volume)." initial condition. Doesn't that make you feel uncomfortable? Must it not make a difference? If the initial value were 6% then nothing would ever change.
 


Dick said:
Your solution never uses the "4% alcohol (by volume)." initial condition. Doesn't that make you feel uncomfortable? Must it not make a difference? If the initial value were 6% then nothing would ever change.

Well yes, id use the initial condition after I have done the differential equation.

So,

-ln |30 - A | = t/100 + C

then put in initial condition. Solve for c = -ln10 (because 4% of 500 is 20)

No? Its not working for me, eeek
 


It looks like it's working fine to me. Now solve for A. Why do you think it's not working? Show the rest. What are you putting in for t? What are you getting for A? What's that in terms of percentages?
 


make sure when you do e^(-ln|30-A|) you get 1/(30-A), everything else is right
 

Similar threads

Differential equation mixing problem
  • · Replies 9 ·
Replies
9
Views
4K
Differential equations incongruecy
  • · Replies 1 ·
Replies
1
Views
2K
Solving a mixing problem with a differential equation
  • · Replies 2 ·
Replies
2
Views
3K
When is the tank empty? [differential equation]
  • · Replies 3 ·
Replies
3
Views
3K
Can someone explain how to setup this differential mixing problem
  • · Replies 2 ·
Replies
2
Views
2K
Mixing Tank, Differential Equations Problem
  • · Replies 11 ·
Replies
11
Views
5K
[Differential equations] Mixing problem.
  • · Replies 2 ·
Replies
2
Views
2K
Simple D.E mixing tank problem
  • · Replies 1 ·
Replies
1
Views
2K
Differential equations problem, flow rates, constantly changing volume
  • · Replies 5 ·
Replies
5
Views
10K
Salt tank differential equation
  • · Replies 3 ·
Replies
3
Views
15K