3. It is common practice for physicians to monitor sounds in the chest using a s

Question

3. It is common practice for physicians to monitor sounds in the chest using a stethoscope. There are two clearly audible heart sounds associated with closure of the tricuspid and mitral valves which induce fluid turbulence upon closure. Using the equation for the Reynolds number below, complete the following problems: 2avp Re where a = the radius of the tube, v = the average velocity, p = density, and-viscosity. For blood, assume p 1060 kg/m' andn-2.78 mPa"s. a.) Estimate the average velocity needed to induce turbulence in the aorta around the aortic valve. State clearly your assumptions (referencing any sources used) and report your answer in m/s. (10 points) b.) Detection of an audible noise (bruit) in the carotid artery has been associated with atherosclerosis (Pickett et al. (2012) Atherosclerosis: Clinical Perspectives Through Imaging, pp. 59-74). Calculate the average velocity that would be needed to induce turbulence in a carotid artery 5mm in diameter. Report your answer in m/s. (5 points)

Explanation / Answer

(a) Assuming that the diameter of internal tube of Aorta at the time of induction of turbulence is 2.5 cm for which Reynolds Number of the Aorta is 3400 alongwith given density and viscosity of the blood, the average velocity needed to induce turbulence is=

(Reynold number* Viscosity)/(Diameter of aorta*density of blood)

=(3400*2.78)/(2.5*1060)

=35.6 cm/sec or 0.356 m/sec

(b) Assumption is that audible noise bruit is high and thus Reynold Number of blood is greater than equal to 1800.

Diameter of Carotid Artery= 5 mm or 0.005 m

alongwith given density and viscosity of the blood, the average velocity needed to induce turbulence in carotid artery after bruit noise is=

(Reynold number* Viscosity)/(Diameter of aorta*density of blood)= (1800*2.78)/(5*1060) m/sec= 0.944 m/sec

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