Question 3 Blood flows through a narrow vessel. The vessel is so narrow that the red blood cells are aligned in single f

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Question 3 Blood Flows Through A Narrow Vessel The Vessel Is So Narrow That The Red Blood Cells Are Aligned In Single F 1 (174.13 KiB) Viewed 60 times

Question 3 Blood flows through a narrow vessel. The vessel is so narrow that the red blood cells are aligned in single file along the centre of the vessel, as shown in the figure below. The capillary has two segments; the first segment has a length L1 = 1 mm and a radius of R, = 6 um. After this point, the radius is reduced to R2 = 4.25 um. Segment 2 has a length 12 = 0.5 mm. The average radius of a red blood cell is Rc = 4 pm. The cells move at a mean velocity 0.1 = 1 mm/s in segment 1, and at Uc2 = 1.4 mm/s in segment 2. The wall shear stress can be approximately as UCK Tw = p R - Rc Where Uc and Ry are the cell velocity and radius in that segment, and Hp = 1 mPa.s is the viscosity of blood plasma. Rc HELISTEST R; R₂ h Figure Q3: Red blood cells flowing through capillary. a) Find the total pressure drop across the capillary. (Hint: you can use the relationship between shear stress and pressure gradient for Poiseuille flow.) (10 marks] b) If the flow rate through the vessel is Q = 3 x 10-6 mL/min, find the effective viscosity, Herr, in each segment (10 marks] c) The viscosity of blood in large vessels is 3 mPa.s. What phenomenon explains the change in effective viscosity in segment 1 compared to the viscosity of blood in large vessels. [3 marks] d) What phenomenon explains the change in effective viscosity in segment 2 compared to the viscosity of blood in large vessels. [2 marks]