Problem 72P

· BIO An Occlusion in an Artery Suppose an occlusion in an artery reduces its diameter by 15%, but the volume flow rate of blood in the artery remains the same. By what factor has th pressure drop across the length of this artery increased?

Solution 72P

Step 1 of 1

We have to find by what factor does the pressure drop across the length of the artery increases if an occlusion reduces its diameter by 15 %.

The pressure drop across the length of the artery can be found using Poiseuille's equation.

where,

volume flow rate

= pressure drop across the length of the artery

= radius of the artery

viscosity of blood

length of the artery

Now, let and be the volume rate before and after the reduction in diameter by 15% of the artery respectively.

=

=

So, = and

But

Hence, =

Solving for

= (

Substituting for

Thus,

= (

= 1.94

Therefore, the pressure drop across the length of the artery increases by a factor of 1.94.