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Poiseuille’s Law describes the pressure drop in an artery of length L and radius r due to the viscosity of blood, where η is the coefficient of viscosity for the fluid and Q is the volume flow rate. According to Poiseuille’s Law, pressure drop would be MOST affected by:A.increasing the coefficient of viscosity by a factor of two.B.increasing the volume flow rate by a factor of two.C.increasing length of the artery by a factor of two.D.reducing the radius of the artery by a factor of two.

Question

Poiseuille’s Law describes the pressure drop in an artery of length L and radius r due to the viscosity of blood, where η is the coefficient of viscosity for the fluid and Q is the volume flow rate. According to Poiseuille’s Law, pressure drop would be MOST affected by:A.increasing the coefficient of viscosity by a factor of two.B.increasing the volume flow rate by a factor of two.C.increasing length of the artery by a factor of two.D.reducing the radius of the artery by a factor of two.

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Solution

Poiseuille’s Law is given by the formula ΔP = 8ηLQ/πr⁴. From this equation, we can see that the pressure drop (ΔP) is directly proportional to the viscosity (η), the length of the artery (L), and the volume flow rate (Q). However, it is inversely proportional to the fourth power of the radius (r⁴).

This means that:

A. If we increase the coefficient of viscosity by a factor of two, the pressure drop will also increase by a factor of two.

B. If we increase the volume flow rate by a factor of two, the pressure drop will also increase by a factor of two.

C. If we increase the length of the artery by a factor of two, the pressure drop will also increase by a factor of two.

D. If we reduce the radius of the artery by a factor of two, the pressure drop will increase by a factor of 2⁴ = 16.

Therefore, according to Poiseuille’s Law, the pressure drop would be most affected by reducing the radius of the artery by a factor of two.

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