Homework Help: D.E mixing problem need help with rate out

1. Apr 9, 2007

HappMatt

1. The problem statement, all variables and given/known data
A large tank initially hold 40 gallons of water. Pure alcohol enters at a rate of 2 Gal/min is well stirred and the mixture leaves at 1gal/min. What will be the concentration when of alcohol when the tank has 80 gallons of fluid in it.

2. Relevant equations
q= amount of alcohol
i have dq/dt=rate in -rate out
rate in=2gal/min of OH
it will take 40 mins to fill to 80 gal
and the thing im wandering about is the rate out.
i currently have
rate out=q/(40+2t), but im thinking maybee its q/(40+t)

as for the rest i think im fine its just this outflow rate im not sure on.

2. Apr 9, 2007

jamesrc

Your second guess for the outflow rate appears correct to me, making your differential equation:
$$\frac{dq}{dt}=2-\frac{q}{40+t}$$

Any reason you are not sure that you would like to discuss?

Don't forget that when you are answering the problem they are asking for concentration of alcohol; your state variable q is currently defined as the amount of alcohol in gallons.

3. Apr 9, 2007

HappMatt

well at first i was thinking of using (40+2t) since that was the initial volume + the flow in but then i thought about how the acutal vol change is just t when you account for the out flow.

as far as the concentration goes what i did was set up the D>E for the quanity of OH in the container then just divid q by (40+2t)

thanks for the help i sortof needed that conformation.