• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Differential Equation mixing problem

  • Thread starter jordan123
  • Start date
Differential Equation mixing problem!!!!!

1. 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?

3. The Attempt at a Solution

This is what ive 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 whats up that would be much appreciated!
 

Dick

Science Advisor
Homework Helper
26,258
618
Re: Differential Equation mixing problem!!!!!

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.
 
Re: Differential Equation mixing problem!!!!!

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
 

Dick

Science Advisor
Homework Helper
26,258
618
Re: Differential Equation mixing problem!!!!!

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?
 
Re: Differential Equation mixing problem!!!!!

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

Related Threads for: Differential Equation mixing problem

Replies
2
Views
4K
Replies
9
Views
1K
Replies
2
Views
8K
Replies
15
Views
8K
Replies
1
Views
4K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top