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ECE_3820_2011_Hw5

ECE_3820_2011_Hw5 - constructed with a diameter of 3 cm...

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ECE 3820: Principles and Practice of BME Homework Set #5 Problem 1: Ritter 3.1. Problem 2: Ritter 3.2. Problem 3 : A patient has a stenotic aortic valve producing a pressure drop between the left ventricle and the aorta. The mean velocity in the left ventricle proximal (upstream) to the valve is 1 m/s, while the mean velocity in the aorta distal (downstream) of the valve is 4 m/s. Compute the pressure drop across the valve. Problem 4 : It is desired to study the fluid dynamics in a coronary artery having a diameter of 3 mm using laser Doppler velocimetry (LDV). However, the resolution of the LDV system is 300 µ m, resulting in a maximum of 10 velocity points across the artery diameter and low accuracy for obtaining wall shear stresses from the fitted velocity profile. To improve the resolution by a factor of 10, a physical model of the artery is
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Unformatted text preview: constructed with a diameter of 3 cm. What flow rate should be used for the model to ensure that the fluid dynamics in the model represent the fluid dynamics in the coronary artery? Assume the working fluid in the model has the same properties as blood: µ =0.035 Poise and ρ =1.07 g/cm 3 . Problem 5 : An incompressible velocity field for blood flow is given as where a is a constant and gravity is in the z direction only. Use the Navier-Stokes equations for Cartesian coordinates to write the pressure gradient function. Remember: k j axy i y x a V ˆ ˆ 2 ˆ ) ( 2 2 + − − = k g j i g ˆ ˆ ˆ − + = z V V y V V x V V t V dt V d z y x ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ =...
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