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Multiple Choice
Which of the following has the greatest effect on blood flow through a blood vessel?
A
The viscosity of the blood
B
The radius of the vessel
C
The pressure at the vessel entrance
D
The length of the vessel
Verified step by step guidance
1
Understand the factors affecting blood flow: Blood flow through a vessel is influenced by several factors, including viscosity of the blood, radius of the vessel, pressure at the vessel entrance, and length of the vessel. These factors are described by the Hagen-Poiseuille equation.
Recall the Hagen-Poiseuille equation: The equation for blood flow (Q) is given as: , where r is the radius of the vessel, ΔP is the pressure difference, η is the viscosity of the blood, and L is the length of the vessel.
Analyze the impact of each variable: The radius (r) is raised to the fourth power in the equation, meaning small changes in the radius have a disproportionately large effect on blood flow. In contrast, viscosity (η), pressure difference (ΔP), and length (L) have linear or less significant effects.
Compare the options: The viscosity of the blood affects flow but not as dramatically as the radius. The pressure at the vessel entrance contributes to ΔP but does not have as significant an effect as the radius. The length of the vessel inversely affects flow but is less impactful compared to the radius.
Conclude: Based on the equation and analysis, the radius of the vessel has the greatest effect on blood flow due to its exponential relationship in the Hagen-Poiseuille equation.