(a) Suppose a blood vessel’s radius is decreased to 90.0% 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? (b) If turbulence is created by the obstruction, what additional effect would it have on the flow rate?

a.)

Step 1 of 3</p>

The factor by which the pressure difference must decrease can be calculated by applying Poiseuille's law which states that the flow rate (Q) of a fluid in a pipe is related to the viscosity

() of the fluid, the pressure gradient between the ends (P), the length (l) and diameter(r) of the pipe by

Where, P = Pressure difference between the ends of the artery in N/m2

r = radius of the artery in m

= Viscosity of the blood in Pas

l = length of the artery in m

Step 2 of 3</p>

Let r1and r2 be the radius of the blood vessel before and after the decrease in blood vessel’s radius to 90% of its original value and P1 and P2 be the pressure difference before and after the decrease in the radius of the blood vessel.

=

The blood flow rate is constant.

Where, Q1and Q2 are the flow rates before and after

the decrease in blood vessel’s radius.

Substituting for Q1 and for Q2

=

==

=

Solving for P2

=

Substituting for

=

=

= 1.52

= 1.52

Therefore,the pressure difference must increase by a factor of 1.52.

b.)