The diameter of a certain artery has decreased by 22% due to arteriosclerosis.
(a) If the same amount of blood flows through it per unit time as when it was unobstructed, by what percentage has the blood pressure difference between its ends increased?
(b) If, instead, the pressure drop across the artery stays the same, by what factor does the blood flow rate through it decrease? (In reality we are likely to see a combination of some pressure increase with some reduction in flow.)
flow rate = (pi/8) * deltaP/(viscosity*L) * r^4. Fill in for point A (before the blockage) and fill in for point B (inside the blockage) and then set equal because flow rate doesn't change (for part (a)).
The Attempt at a Solution
For (a), I know that everything is constant except for deltaP and r, so the equation can be simplified down to deltaP of B/delta P of A = (r of A)^4/(r of B)^4 which is, in turn, = to (1/.78)^4, or at least I think it is. That gives a percentage of 2.7% which is incorrect.
For (b), I am similarly able to reduce the equations down to (.78/1)^4. That gives a factor of .37 drop in blood flow rate. Once again, I'm incorrect.
I'm clearly not doing something correctly here. Can anyone shed a bit of light? Thank you.