Certified Registered Nurse Anesthetist (CRNA) Practice Exam

According to Poiseuille's law, what happens to airflow resistance if the radius of the conducting airway is reduced from 4mm to 2mm?

1. It decreases by half

2. It remains the same

3. It increases four-fold

4. It increases sixteen-fold

The correct answer is: It increases sixteen-fold

Poiseuille's law states that the airflow resistance in a tube is inversely related to the fourth power of the radius of the tube. This relationship can be expressed mathematically as: Resistance ∝ 1 / r^4 Where 'r' is the radius of the conducting airway. When the radius of the airway is decreased from 4 mm to 2 mm, we can calculate the change in resistance as follows: 1. Calculate the original resistance with a radius of 4 mm: Resistance at 4 mm = k / (4 mm)^4 2. Calculate the new resistance with a radius of 2 mm: Resistance at 2 mm = k / (2 mm)^4 Now, comparing the two: - Resistance at 4 mm: k / 256 - Resistance at 2 mm: k / 16 To find the change in resistance, we can set up a ratio of the two resistances: Resistance at 2 mm / Resistance at 4 mm = (k / 16) / (k / 256) This simplifies down to: 256 / 16 = 16 This shows that the resistance increases by a factor of 16 when the radius is reduced from