Airway Model: Why a Little Narrowing Matters
A flow model that shows why small changes in airway width cause large changes in airflow.
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Standards
HS-LS1-2 — Develop and use a model to illustrate the hierarchical organization of interacting systems that provide specific functions within multicellular organisms.
MS-LS1-3 — Construct an argument supported by evidence that the body is a system of interacting subsystems.
Why Does This Matter?
Childhood asthma rates in Detroit are among the highest in Michigan, especially in neighborhoods near highways and industry. During an asthma attack the airways swell and tighten, and a small change in their width sharply reduces airflow. A simple drain model lets you measure that effect directly.
Objective
Measure how fast water drains through tubes of different diameters and use the pattern to explain why narrowed airways make breathing difficult.
Materials
- A 2-liter plastic bottle with a hole near the bottom sized for the tubing (teacher-prepared), and modeling clay to seal it
- Three lengths (50 cm each) of clear vinyl tubing with different inner diameters, for example 3, 6, and 10 mm
- Measuring cup or graduated cylinder, a catch bucket, and a stopwatch
- Water, a marker, and a calculator
Safety: Water on the floor is a slip hazard — work over a tray or bucket and wipe spills immediately. This model uses water only; never blow through shared tubing.
Procedure
- Mark a fill line on the bottle that holds 500 mL. Attach the narrowest tube to the hole and seal around it with clay. Hold the free end of the tube lower than the bottle, over the bucket, and pinch it closed.
- Fill the bottle to the line. Release the tube and time how long it takes to collect 250 mL. Repeat once more and average the two times.
- Repeat with the medium and wide tubes, using the same fill line and the same tube length and height.
- Calculate the flow rate for each tube (250 mL ÷ average time). Then calculate how many times larger each flow rate is compared with the narrowest tube.
- Fill in the last two columns using the idealized predictions: flow is proportional to (radius)² for a short opening and to (radius)⁴ for long, narrow tubes.
Data Table
| Inner diameter (mm) | Trial 1 time (s) | Trial 2 time (s) | Average time (s) | Flow rate (mL/s) | Flow vs. narrowest | Predicted by radius² / radius⁴ |
|---|---|---|---|---|---|---|
| 1.0 | 1.0 / 1.0 | |||||
Analysis Questions
- How did the flow rate change as the tube diameter increased? Was the change proportional to the diameter?
- Compare your measured flow ratios with the radius² and radius⁴ predictions. Which was closer, and why might real results fall between the two?
- Use your results to explain why airway swelling and mucus during an asthma attack can cut airflow dramatically even though the airway only narrows a little.
- List two ways a family or school could reduce asthma triggers in the places where students spend time.