Dimensional Analysis...

[Orsorum]

Anyone good at this? I need some help with a hw prob.

 

[HomeBrewerDude]

what class?

 

[Evadman]

Post the question.

 

[Orsorum]

It's for a mathematical modeling class... just confused as to some of the exact terminology, I guess.

Simplified Chemostat. Consider a simplified chemostat, where substrate is pumped into the system at a concentration Si and a flow rate D. Bacteria in the chemostat consume the substrate and reproduce. The overflow is pumped out at the same rate D. Let S(t) represent the concentration of the substrate at time t, and let B(t) represent the concentration of the bacteria. This system can be modeled like so:
dS/dt = D(Si - S) - (u1/y1)SB
dB/dt = (u1)SB - DB

(a) fundamental units are time, [t], substrate concentration, , and bacteria concentration, [B.]. In order that the system be dimensionally homogeneous, what are the dimensions of each of the appearing parameters?
(b) What are the characteristic scales for each of the fundamental units? That is, what combination of parameters yield quantities with dimensions [t], , and [B.]?
(c) Make the change of variables t = [t]t, S = s, B = [B.]b. Non-dimensionalize the system of differential equations. What are the natural choices for [t], and [B.]?
(d) Identify a linear combination u = c1s + c2b of the nondimensial quantities s and b, so that du/dt obeys a simple linear differential equation. Find the solutions for u.

EDIT: Finally... stupid HTML tags.

 

Ugh, we did this in introductory high school chemistry class. My teacher used to refer to D.A. as, "DAAAAAAAAAAAAAAHHHHHHHHHHHHHHHHH!!!!!!!!!!" I was an expert at it but only at converting meters to inches and other simple stuff. Sorry I can't help you.

 

[Orsorum]

Originally posted by: JuMpR629
Ugh, we did this in introductory high school chemistry class. My teacher used to refer to D.A. as, "DAAAAAAAAAAAAAAHHHHHHHHHHHHHHHHH!!!!!!!!!!" I was an expert at it but only at converting meters to inches and other simple stuff. Sorry I can't help you.

It's all good... thanks anyway.

 

[Yossarian]

The answer is... four??

 

[Orsorum]

Originally posted by: PipBoy
The answer is... four??

42.

 

[Orsorum]

So, for (a)... I think the parameters he's referring to are D, u1 and y1.

If that's the case, then it all works out to where [D] = 1/[T], [u1] = 1/[T], and y1 = [B.]/.

Still working on (b)-(d).

 

[Orsorum]

Originally posted by: yamahaXS
what class?

Amath 383, at the University of Washington.

 

[Orsorum]

Bump.