Blood flows along a straight vessel, that has an internal diameter of 1 mm. The blood...

  

Transcribed Image Text:

Blood flows along a straight vessel, that has an internal diameter of 1 mm. The blood has a density of 1200 kg/m, and the viscosity depends on haematocrit level, as shown in Figure Q1. a) Find an expression for the wall shear stress as a function of flow rate. (Note: you are not required to derive the velocity profile from the Navier-Stokes equation) b) When the viscosity increases, blood vessels can dilate (increase their diameter) to ensure that the magnitude of the wall shear stress remains constant. If the haematocrit increases from 40% to 50%, find the increase in the internal vessel diameter. You may assume the flowrate does not change. c) In some conditions like Sickle Cell Disease, blood vessels cannot dilate when the viscosity increases. If the haematocrit increases from 40% to 50%, find the percentage change in wall shear stress for a patient with Sickle Cell Disease. Viscosity [CP] 5 4.5 4 3.5 3 2.5 2 1.5 20 25 30 40 45 50 55 60 Haematocrit [%] Figure Q1: Variation in blood viscosity with haematocrit. 35 Blood flows along a straight vessel, that has an internal diameter of 1 mm. The blood has a density of 1200 kg/m, and the viscosity depends on haematocrit level, as shown in Figure Q1. a) Find an expression for the wall shear stress as a function of flow rate. (Note: you are not required to derive the velocity profile from the Navier-Stokes equation) b) When the viscosity increases, blood vessels can dilate (increase their diameter) to ensure that the magnitude of the wall shear stress remains constant. If the haematocrit increases from 40% to 50%, find the increase in the internal vessel diameter. You may assume the flowrate does not change. c) In some conditions like Sickle Cell Disease, blood vessels cannot dilate when the viscosity increases. If the haematocrit increases from 40% to 50%, find the percentage change in wall shear stress for a patient with Sickle Cell Disease. Viscosity [CP] 5 4.5 4 3.5 3 2.5 2 1.5 20 25 30 40 45 50 55 60 Haematocrit [%] Figure Q1: Variation in blood viscosity with haematocrit. 35