Calculating the equation for a float in a rotameter

[akhan90]

I'm trying to design a rotameter, a flowmeter consisting of a float in a tube of increasing area (like a cone). I know the equations equating drag with gravity, but I'm more interested in the equation of the float's velocity over time, just as steady state flow begins (so x(0)=0)

Because the velocity of fluid is changing at different points in the meter, I don't exactly know how to set up a force balance equation, if that's even what I need to do. I would guess velocity would be in terms of both position and time, but I'm not certain.

 

[Nidum]

The working principle of the float rotameter is well known . A simple search will yield a large amount of useful information .

Please come back if you have any specific difficulties .

 

[akhan90]

The working principle of the float rotameter is well known . A simple search will yield a large amount of useful information .

Please come back if you have any specific difficulties .

I know the working principle of equating drag and gravity to find the final position. My difficulty has to do with the initial phases of motion prior to when the float reaches steady state, in other words, when flow isn't maintained long enough for the rotameter float to reach steady state position.