Question

If the radius of a blood vessel drops to 80.0% of its original radius because of the buildup of plaque, and the body responds by increasing the pressure difference across the blood vessel by 10.0%, what will have happened to the flow rate? The flow rate will have changed to _______ % of its original value.

Answer 1

40.96%

Solution:

As per the question:

If the original radius be 'r' and the initial pressure difference be 'P':

After the drop, radius:

r' = 0.8r

After rise in pressure:

P' = 0.1 P

Now,

Rate of flow is given by:

R ∝
`r^(4)P`

Thus

`(R')/(R) = ((0.8r)/(r))^(4)(0.1P)/(P)`

R' = 40.96%