# Open integration problem

1. May 1, 2010

### chronicals

1. The problem statement, all variables and given/known data
The relative velocity of two small spheres subjected to a constant force in a liquid is given by u = uo/f where f is the drag correction factor and u0 is the relative velocity of the spheres when they are far apart. The drag coefficient factor, f, is a function of (r/a) where a is the radius of each sphere and r is the center-to-center distance. Given the following data for the correction factor estimate the time at which it takes the spheres to travel apart from r=22 μm to r=32 μm when u0=1 mμ/s and a=10 μm
using an appropriate open integration formula. (Hint: dt=dr/u )
r/a: 2.1 2.5 3.0 3.5
f: 4.03 1.72 1.37 1.24

2. Relevant equations

3. The attempt at a solution
I don't understand the problem, can you explain what i should do firstly?

2. May 1, 2010

### gabbagabbahey

Let's imagine for a second, that you were given the exact functional form of $f\left(\frac{r}{a}\right)$....what would you do to find the time it takes the spheres to travel apart from r=22 μm to r=32 μm?

3. May 2, 2010

### chronicals

Re: integration problem

Can you give me the function which i should integrate, the problem is very complex and difficult to solve for me

Last edited: May 2, 2010
4. May 2, 2010

### gabbagabbahey

Again, all I'm asking is that if I gave you $f\left(\frac{r}{a}\right)$...what would you do to find the time it takes the spheres to travel apart from r=22 μm to r=32 μm?