Solve ODE Mixture Question: 100 Gal Water Tank

  • Thread starter Thread starter cue928
  • Start date Start date
  • Tags Tags
    Mixture Ode
Click For Summary
SUMMARY

The discussion focuses on solving a first-order ordinary differential equation (ODE) related to a 100-gallon water tank where a sugar-water mixture enters at a rate of 3 gallons per minute, containing 0.2 lbs of sugar per gallon. The rate of sugar entering the tank is calculated as 0.6 lbs/min, while the outflow rate is represented as A/100, where A is the amount of sugar in pounds. The user initially miscalculated the integration constant, leading to discrepancies in the final sugar content after 20 minutes, which should be 9.0348 lbs instead of the incorrect 16.##.

PREREQUISITES
  • Understanding of first-order ordinary differential equations (ODEs)
  • Familiarity with integration techniques and integrating factors
  • Knowledge of fluid dynamics principles, specifically mixing processes
  • Basic calculus skills, particularly in solving differential equations
NEXT STEPS
  • Study the method of integrating factors for solving first-order ODEs
  • Explore fluid dynamics concepts related to mixing and flow rates
  • Practice similar ODE problems involving inflow and outflow rates
  • Learn about the application of differential equations in real-world scenarios, such as chemical mixing
USEFUL FOR

Students and professionals in mathematics, engineering, and chemistry who are interested in solving differential equations and understanding fluid dynamics in mixing processes.

cue928
Messages
129
Reaction score
0
Tank w/ 100 gal pure water. At time = 0, sugar/water mixture with .2 lbs of sugar per gallon enters at 3 gal/ minute. Drain opened at bottom allows sugar solution to leave at 3 gal per minute. Perfect (lol) mixing occurs.

I show the following:
Rate in: .2 x 3 = .6
Rate out: x/100
Volume: 100

dA/dt = .6 - A/100; I get an integrating factor of e^x/100. It asks what will the sugar content be after 20 minutes. I came up with a C value of 19.4. I get 16.##, they get 9.0348. Any idea where I'm going wrong?
 
Physics news on Phys.org
hi cue928! :smile:
cue928 said:
Tank w/ 100 gal pure water. At time = 0, sugar/water mixture with .2 lbs of sugar per gallon enters at 3 gal/ minute. Drain opened at bottom allows sugar solution to leave at 3 gal per minute. Perfect (lol) mixing occurs.
…
dA/dt = .6 - A/100

oooh :cry: … what happened to the (second) 3 gal per minute? :redface:
 

Similar threads

ODE problem -- Find the amount salt in the tank as water flows through it
  • · Replies 3 ·
Replies
3
Views
4K
Find the quantity of salt in the tank?
  • · Replies 6 ·
Replies
6
Views
5K
When is the tank empty? [differential equation]
  • · Replies 3 ·
Replies
3
Views
3K
Simple D.E mixing tank problem
  • · Replies 1 ·
Replies
1
Views
2K
The Mixing Problem: Understanding the Dilution of Brine in a Tank
  • · Replies 4 ·
Replies
4
Views
2K
Solving Mixture Problem ODE Homework
  • · Replies 15 ·
Replies
15
Views
4K
Differential equations capacity tank problem (chemical solutions) mixture
  • · Replies 1 ·
Replies
1
Views
9K
Water Tank Differential Equation Problem
  • · Replies 3 ·
Replies
3
Views
8K
Find the quantity Q(t) of salt in the tank?
  • · Replies 1 ·
Replies
1
Views
2K
Solution pumped into a tank problem.
  • · Replies 16 ·
Replies
16
Views
4K