Euler's Method With Mass Balance o.d.e's

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SUMMARY

The discussion centers on the application of Euler's Method to solve a mass balance ordinary differential equation (ODE) in a mathematical modeling context. The user is struggling with the formulation of the differential equation due to the presence of the term sqrt(h1-h2), which results in an imaginary number because h1 is less than h2. The user seeks assistance in correctly simplifying the equations to make them solvable using Euler's Method, particularly for predicting tank levels after 5 seconds.

PREREQUISITES
  • Understanding of Euler's Method for numerical solutions of ODEs
  • Familiarity with mass balance principles in fluid dynamics
  • Basic knowledge of differential equations
  • Ability to interpret mathematical diagrams and variables
NEXT STEPS
  • Research the correct formulation of mass balance equations in fluid systems
  • Study examples of Euler's Method applied to similar ODEs
  • Learn how to handle square root terms in differential equations to avoid imaginary results
  • Explore numerical stability considerations when using Euler's Method
USEFUL FOR

Mathematics students, engineers involved in fluid dynamics, and anyone interested in numerical methods for solving differential equations.

Sam223344
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Hi

I'm doing a practice paper for a past mathematical modelling exam. I've attached the problem

What I'm having trouble with is simplifying the equations and variables into a differential equation that is solvable with Euler's Method.

What I have currently is the sqrt(h1-h2) in the equation which leads to an imaginary number so I don't think I have done it correctly. ( As h1<h2..I think the diagram is also misleading)

If someone could help me out with getting the right equation I should(hopefully) be able to do the next part.

Thanks

I'm posting this is another forum as well, need help asap.

P.S the second question doesn't need to be attached, it is:
Use Euler's method to make a single step to predict the levels in both tanks after 5 seconds.
 

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    Questionpart1.jpg
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Last edited:
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Euler's Method With Mass Balance o.d.es

I'm doing a practice paper for a past mathematical modelling exam. I've attached the problem

What I'm having trouble with is simplifying the equations and variables into a differential equation that is solvable with Euler's Method.

What I have currently is the sqrt(h1-h2) in the equation which leads to an imaginary number so I don't think I have done it correctly. ( As h1<h2..I think the diagram is also misleading)

If someone could help me out with getting the right equation I should(hopefully) be able to do the next part.

Thanks

I also posted this is the differential equation forum but with only 6 people viewing...
 

Attachments

  • Quest1.jpg
    Quest1.jpg
    30.6 KB · Views: 576


This is what I have but its the square root of a negative number that is confusing me
 

Attachments

  • Equations.jpg
    Equations.jpg
    14 KB · Views: 507

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