Learning Objective:
Understand and apply the formula for vascular resistance (R), which describes the relationship between pressure, flow, and vessel characteristics in the circulation.

Formulas:

and by Poiseuille’s Law:

Explanation:

• = Resistance
• = Driving Pressure (difference between arterial and venous pressure)
• = Flow (blood flow rate)
• = Viscosity of blood
• = Length of the vessel
• = Radius of the vessel

From Poiseuille’s law, resistance is inversely proportional to the fourth power of the radius — even a small decrease in vessel radius greatly increases resistance.

Key Relationship:
→ small changes in radius have large effects on resistance.

Example:

If vessel radius decreases by 50%:

✅ Answer: Resistance increases 16-fold when radius is halved.