Register to reply

Mixture problem. How to solve for C?

by Jeff12341234
Tags: mixture, solve
Share this thread:
Jeff12341234
#1
Feb22-13, 09:13 PM
P: 179
I need to solve for C. I know it's probably simple but i don't remember how to. This is what I have so far:
Phys.Org News Partner Science news on Phys.org
New model helps explain how provisions promote or reduce wildlife disease
Stress can make hard-working mongooses less likely to help in the future
Grammatical habits in written English reveal linguistic features of non-native speakers' languages
Chestermiller
#2
Feb22-13, 10:33 PM
Sci Advisor
HW Helper
Thanks ∞
PF Gold
Chestermiller's Avatar
P: 5,043
Because the volume flow rate entering is different from the volume flow rate leaving, you need to write down two differential equations, rather than 1:

Volume Input - Volume Output = accumulation for the volume of fluid in the tank

Chemical X Input - chemical X Output = accumulation for chemical X in the tank

If V(t) is the volume of fluid in the tank at time t, fin is the volumetric flow rate of fluid in, and f_out is the volumetric flow rate of fluid out, what is the differential equation for V?

If C(t) is the concentration of chemical X within the tank at time t, and C_in is the concentration of chemical X in the feed to the tank, what is the differential equation for the rate of change of total chemical X in the tank?

The next step is to multiply the differential equation for V by C, and subtract the resulting relationship from the mass balance on chemical X.
Jeff12341234
#3
Feb22-13, 10:46 PM
P: 179
I don't follow.. The way I did it is the way the professor instructed us and the steps match the steps in his example. To solve for C, I now realize from an example in the book that A(0)=35. With that information, I can solve for C.


Chestermiller
#4
Feb23-13, 07:41 AM
Sci Advisor
HW Helper
Thanks ∞
PF Gold
Chestermiller's Avatar
P: 5,043
Mixture problem. How to solve for C?

OK. I see what you did, and, of course, it is right. But, here's my alternate version to consider:

[tex]\frac{dV}{dt}=f_{in}-f_{out}[/tex]
[tex]\frac{d(VC)}{dt}=f_{in}C_{in}-f_{out}C[/tex]
Multiply the first equation by C and subtract it from the second equation:

[tex]V\frac{dC}{dt}=f_{in}(C_{in}-C)[/tex]

where [itex]V=V_0+(f_{in}-f_{out})t[/itex]
So,

[tex]\frac{dC}{(C_{in}-C)}=f_{in}\frac{dt}{V_0+(f_{in}-f_{out})t}[/tex]


Register to reply

Related Discussions
Gas mixture problem Biology, Chemistry & Other Homework 9
Mixture Problem ODE Calculus & Beyond Homework 15
Mixture Problem (pls help) Calculus & Beyond Homework 0
Mixture problem Precalculus Mathematics Homework 2
Gas mixture problem! Biology, Chemistry & Other Homework 3