quiz2

# quiz2 - Harvard-MIT Division of Health Sciences and...

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Unformatted text preview: Harvard-MIT Division of Health Sciences and Technology HST.542J: Quantitative Physiology: Organ Transport Systems Instructors: Roger Mark and Jose Venegas MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departments of Electrical Engineering, Mechanical Engineering, and the Harvard-MIT Division of Health Sciences and Technology 6.022J/2.792J/BEH.371J/HST542J: Quantitative Physiology: Organ Transport Systems QUIZ 2 Tuesday, April 6, 2004 Name: Problem 1 (20 min) One method for determining the degree of ﬂow obstruction produced by a stenosed aortic valve is to measure pressures simultaneously inside the left ventricle and at a point several aortic diameters downstream of the valve. In this question you will be asked to develop the relationship between these pressures and the cross-sectional area of the valve. (See Figure 1.1.) Figure 1.1: a a (2) (1) (3) Surface a–a Control volume A s P V v Turbulent mixing zone Valve area v, Ventricle Pressure P 2 Area A , Pressure P 3 A. Find the pressure, P 2 , at the exit of the stenosed valve (2) assuming ﬂow between (1) and (2) to be inviscid and steady . (Although the real ﬂow is unsteady, the effects of unsteadi- ness in this calculation are small.) You may express P 2 in terms of the instantaneous ﬂow rate through the valve, Q , the pressure in the ventricle, P v (where the velocity, V v , can be assumed to be zero), the area of the valve,...
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quiz2 - Harvard-MIT Division of Health Sciences and...

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