A coronary blood vessel has an axisymmetric contraction because of a atheroscler

Question

1. A coronary blood vessel has an axisymmetric contraction because of a atherosclerotic plaque build up (stenosis). Given conditions of upstream velocities of 10 cm/s during diastole and 15 cm/s during systole, correspondingly, find the corresponding diastolic and systolic velocities at the stenosis throat and the pressure gradient between the upstream and the stenosis throat for diastolic and systolic conditions (rblood = 1.057 g/cm3). What is the additional pressure that the pumping heart has to develop over the normal diastolic and the systolic pressures (80 mmHg and 120 mmHg correspondingly) due to the presence of the stenosis? (Diameter of regular vessel (D=3mm))(Diameter of stenosis (d=1mm))

Explanation / Answer

AV = Constant

Therefore

A*0.13 = (A/6)*V

V = 0.78 m/sex

According to the ernoulli Equation

P + pgh + 0.5*p*v^2 = Constant

Therefore

Pressure Difference = 0.5*p*(v^2 - v1^2)

= 0.5*1060*(0.78^2 - 0.13^2)

= 313.495 Pa

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