Question

Consider the arterial stenosis from Quiz 3, where growth of an atherosclerotic plaque has caused the diameter of the blood vessel to be reduced by 80%. This region is labeled “B” in the image below. Assume incompressible and steady flow in the vessel. Model all regions of the vessel as a rigid, impermeable conduit.

Provide the solution (in Pa and rounding to the nearest unit) for the pressure difference between points A and B based upon a vessel diameter of 6.5 mm and a volumetric flow of 6.6 mL/min at point A.  Let the blood density be 1050 kg/m^3.

Answer 1

continuity equation flow is steady, incompressible. Bernoulli theorem and Can be used. un velocity of a velocity of blood at A VB Velocity of blood at B. A area of vessel at a Be area of vessel at B. given that B = AX20 = continuity equation. VA. A = UBB VA A NB-A B = Ax20 - 2 (80% is reduced). given that [SUA = Ve] & O. Now Bernoullis equation. PA + PUA? + sig ha - PB+ five & sights head team can be neglected because both A & B are at same posizontal bine. PA - PB = 8. (VB² va )

PA - PB = . ( 25 VA? - VAP) f. 24. VA? PA-Po= given is flow sale a 6.6 mL/min a = 6.68106 m3 60 second ( Q H x70-7 wi/second] A = Tida Q = VANA A = TX 6-5²x10-6 Halot - VAX B x 6.5x15 - pixy 10XTX - VA 6.52 (VA= 8.31x103 mis } & this value above putting this value above. PA - PB = 1050 x 24 x 3.31² x 106 PA - PR = 0.188 Pa] Answer.