Question

There are two carotid arteries that feed blood to the brain, one on each side of the neck and head. One patient's carotid arteries are each 11.2 cm long and have an inside diameter of 5.3 mm . Near the middle of the left artery, however, is a 2.0-cm-long stenosis, a section of the artery with a smaller diameter of 3.2 mm .

For the same blood flow rate, what is the ratio of the pressure drop along the patient's left carotid artery to the drop along his right artery?

The density of the blood taken is 1060 kg/m^3.

Answer 1

The Poiseuille equation is, 8uLQ 兀R The pressure difference between the two end is ΔΡ , îength is L volumetric flow rate is Q, and the radius of the pipe is R For the left artery, dynamic viscosity is : 8ux (0.0928(0.02) π( 2.65 x10" ) 7 1 π(1.6×10-3 For the right artery, APSOx(0.112) x(2.65 x10-3) For the case of same flow rate, (0.092)(0.02) (265×10-3) (16× 10 1.6x103 ag AP - 0.112) (2.65x10-3 =2.16 The ratio of the pressure drop along the patient's left carotid artery to the drop along the his right artery is 2.16