In this experiment, which variable is kept constant while the other is varied?

In this experiment, which variable is kept constant while the other is varied?

• A. Blood vessel radius is kept constant and blood vessel length is varied.
• B. Blood vessel length is kept constant and blood vessel radius is varied.
• C. Both radius and length are kept constant.
• D. Both radius and length are varied.

Answer: (A)

In a setup that uses Poiseuille’s relationship, flow through a vessel depends on its radius and its length: Q = (π ΔP r^4)/(8 μ L). This means radius has a strong effect (to the fourth power) and length has an inverse effect. To study how changing one geometric factor influences flow while keeping the other fixed, you would fix the radius and vary the length. This isolates the impact of length on flow and resistance, since keeping r constant removes its dominant effect. If you kept length fixed and varied radius, you’d be examining the radius effect instead. If both were kept constant or both varied, you wouldn’t be able to isolate a single variable.

In a setup that uses Poiseuille’s relationship, flow through a vessel depends on its radius and its length: Q = (π ΔP r^4)/(8 μ L). This means radius has a strong effect (to the fourth power) and length has an inverse effect. To study how changing one geometric factor influences flow while keeping the other fixed, you would fix the radius and vary the length. This isolates the impact of length on flow and resistance, since keeping r constant removes its dominant effect. If you kept length fixed and varied radius, you’d be examining the radius effect instead. If both were kept constant or both varied, you wouldn’t be able to isolate a single variable.