3 3. (35 points) A stenosis is a narrowing of a blood vessel or valve. Stenosis of a blood vessel arises druing artherosclerosis and could occlude an artery, depriving the tissue downstream of oxygen. Further, the fluid shear stresses acting on the endothelial cells lining blood vessels mayh affect the expression of genes that regulate endothelial cell function. Such gene expression can influence whether the stenosis grows or not. Consider a symmetric stenosis as shown in the figure below. Assume that the velocity profile within the stenosis of radius Ri(z) has the same shape as the profile outside the stenosis and is represented as 𝑣𝑧𝑟 =𝑣?𝑎𝑥1−2?2Outside the stenosis, the radius equals Roand the maximum velocity is constant. Within the stenosis, the radius of the fluid channel R(z) equals ? 𝑧 =?01−0.51−4𝑧21/2The origin of the z axis is the midpoint of the stenosis. (a) Develop an expression for vmaxin a stenosis in terms of the volumetric flow rate Q, cylindrical tube radius Ro, and the distance along the stenosis 𝐿. Hint: You might want to begin with ?=𝑣 ∙ ? 𝑑𝐴=𝑣𝑧?02𝜋0𝑟𝑑𝑟𝑑𝜃𝑟𝐿𝑧.