   ### Abstract

The objective:

The purpose of my experiment is to determine how the rate of flow of a liquid through a tube is affected by the following factors: (a) pressure driving the flow, (b) the length of the tube and (c) the diameter of the tube. I became interested in this topic when I learned that heart disease results when plaque reduces the diameter of blood vessels, causing a dramatic decrease in flow rate. This topic is of interest because the American Heart Association estimates that heart disease costs the U.S. economy nearly half-a-trillion dollars each year.

### Methods/Materials

I modeled the human circulatory system using a set of latex tubes, and a large container filled with water. The latex tubes were connected to the side of the container, via a valve.

I investigated flow rate dependence on

(a) pressure by changing the height of the water in the container,

(b) tube length using a set of latex tubes of the same diameter, but different lengths, and

(c) tube diameter, using a set of latex tubes of the same length, but different diameters.

I measured the flow rate by determining the amount of time (delta_T) taken for a small volume of water (delta_V) to drain from the container through the tube under investigation.

The flow rate Q was calculated from the ratio delta_V/delta_T. Since the flow rate can be fast I used a high-definition camcorder to record the change in the height of the water in the container. I viewed the video on my computer in slow motion, and obtained accurate readings of delta_T, and delta_V.

### Results

I collected data at 25 conditions, and repeated each measurement 3 times. So I extracted a total of 75 data points from 75 video clips. From this data, I found that the flow rate

(a) increases with increasing pressure (agreed with hypothesis),

(b) decreases with increasing length (contradicted hypothesis), and

(c) increases dramatically with increasing diameter (agreed with hypothesis). My results are in good agreement with the Hagen-Poiseuille Law.

### Conclusions/Discussion

I found that a change in tube diameter can dramatically change the flow rate of water. For example, I found that when tube diameter decreases by a factor of 2.65x flow rate decreases by a factor of 18x! This explains why a decrease in blood vessel diameter can be very harmful to health. By exercising more and changing our eating habits we can reduce plaque in our blood vessels.