# Flow Rate of a Deflation Balloon

1. Sep 6, 2009

### wuyx724

A drug delivery infusion pump is made out of thick synthetic rubber and has a very small outlet. The balloon pump is filled with 500mL liquid drug and is now inflated into a ball shape. The drug will exit from the very small outlet at a nearly (but not always) constant flow rate of 5mL/hr (takes 100hr to deplete).

How can I derive the flow rate as a function of time?
I'd also like to know how the temperature and drug viscosity affect the flow rate.

Someone suggested me to use Poiseuille-Hagen equation, but I need to know more details, especially how I can relate the flow rate to time and establish a model.

Your insight will be highly appreciated!

2. Sep 12, 2009

### hhn2002

the flow rate is constant meaning it remains at 5ml/hr until 100hr is surpassed. so i'd be a piecewise function that looks like this:

given x is time in hours and y is in ml/hr
if 0<x<100 then y=5
if x>100 then y=0

the temperature and viscosity are almost always related in such a manner
as temperature rises viscosity drops and vice-versa
and if viscosity drops then flow rate is usually increased.