# Suppose a blood vessel's radius is decreased to 87% of its original value by plaque deposits and...

## Question:

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?

## Poiseuille's Flow in Circular Tubes :

Considering the flow of a fluid to be laminar and flowing inside a circular tube, we get the Poiseuille's formula.

{eq}Q =\displaystyle \frac{\pi \Delta P R^4}{8 \eta L} {/eq}

where

• Q = discharge volume flow rate
• {eq}\Delta P {/eq} = pressure difference between the ends of the pipe
• R = internal radius of pipe
• L = length of pipe (m)
• {eq}\eta {/eq} = viscosity of fluid

## Answer and Explanation:

The initial radius of the blood vessel be R.

Now, due to the accumulation of plaque, it is decreased to 87% of its original value ie its new radius...

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