Question

Does anyone know of any methods other than using differential equations to solve a mixing tank problem? A question ask me to check my answer using a method other than using DE.

Answer 1

Well could you post an example of what you want solved?

Answer 2

It's a modelling question.
There is a dam with a volume of 49 cubic metres. Water flows out of this into one of the creeks. Salt water with salt content of 30kg/m3 flowed into the dam at 0.68m3/s and mixed with the fresh water. The mixed water flowed out at the same rate. Flag tail in the dam can tolerate salinity up to 14kg/m3. How long after the flow starts can the fish survive in the dam?

Answer 3

It ends up being:
\[\frac{ dQ }{ dt }=20.4-0.0139Q\]

Answer 4

fill a tank up with some stuff, poke a hole in it.

Answer 5

watch a clock.

Answer 6

:)

Answer 7

So you really can't think of any other mathematical methods?

Answer 8

I didn't want to resort to experiments.

Answer 9

nspire - heck I'm thinking but if you want an instantaneous answer then forget it - yep use that calculus.
:-)

Answer 10

I'm sorry, take all the time in the world. I appreciate your effort a lot.

Answer 11

Well shucks thanks

Dam 49 cubic metres.
Dam outflow = ???
Dam inflow = Salt water with 30kg/m3 salt @ 0.68m3/sec mixes with fresh water
Flag tail tolerate no greater than 14kg/m3 salinity
How long after the flow starts can the fish survive in the dam?

Do we only need to know about the concentration of the dam having salinity = or greater than 14 kg/m³

Answer 12

Yes, i have the answer for outflow and final using calculus.

Answer 13

\[Q=1470(1-e^{-0.0139t})\]

Answer 14

Outflow = 0.0139Q Kg/s

Answer 15

I'm sorry. I think I'm too tired to be working on this. - I spent the last day and a half recovering from a computer crash.

Answer 16

It's fine, i appreciate the effort.
Thanks for trying.

Answer 17

wow thanks - that computer carsh really tuckered me out sorry
:-(

Answer 18

lol "I didn't want to resort to experiments."
sorry man I dont know any other way, but im sure someone on here will help you soon enough

Answer 19

Instead of solving the DE analytically, you can solve it numerically. There are numerous methods available. You will probably need to resort to computer programming, or using computer algebra. It's kind of a numerical experiment, taking small steps at a time.

For relative simple, and/or researched problems, analytic method like what you've done is probably still the best way, and more accurate.

Answer 20

Thanks i will look into numerical DE solving. But I think that what my teacher wants is to avoid differential equations altogether. Which is quite an ask because i have no idea how else the question can be answered.