5. (25 pt) A patient presents with severe abdominal pain. Upon examination, it is found that he is suffering from a large abdominal aortic aneurysm located approximately 6 cm below the level of the renal arteries. The aneurysm measures 7 cm in diameter at its midplane.

a) Assuming the patient is standing, and ignoring inertial effects and viscous losses, useBernoulli’s equation to calculate the blood flow velocity [in cm/s] and pressure [in mmHg] at the aneurysmal midplane: (5 pt)

1. i) during systole
2. ii) during diastole

NOTE: – assume an average BP of 120/80 mmHg [systolic pressure/diastolic pressure]

– at the level of the renal arteries, the normal aortic diameter is 2 cm and the

normal flow rate is approx. 4.5 L/min (systole) and 1.8 L/min (diastole)

– assume the aorta maintains the same diameter during systole and diastole – conversion factor: 1 mmHg = 1330 dynes/cm2

1. b) Modeling the aneurysm as a thin-walled spherical pressure vessel, calculate the stress per unit wall thickness in the vessel walls (i.e. the hoop stress) during systole and diastole. (10 pt)
2. c) Repeat parts (a) and (b) for the case in which the patient is lying down horizontally. (5 pt)
3. d) Comment on the results. (5 pt)