# Problem: Suppose a blood vessel's radius is decreased to 87% of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase?

###### FREE Expert Solution

Poiseuille’s law:

$\overline{){\mathbf{Q}}{\mathbf{=}}\frac{\mathbf{\pi }\mathbf{∆}\mathbf{P}{\mathbf{r}}^{\mathbf{4}}}{\mathbf{8}\mathbf{\eta }\mathbf{l}}}$, where Q is the flow rate, P is pressure, r is the radius, η is fluid viscosity, and l is the length of tubing.

In this question, flow rate Q, fluid viscosity η, and the length of the tubing l, are kept constant.

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###### Problem Details

Suppose a blood vessel's radius is decreased to 87% of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase?