Midterm Exam 2004 solutions.doc

# 10 on taking the limit of the following expression as

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10. On taking the limit of the following expression as 0 r , 0 ) ( 2 2 r r r r r r r r one obtains: a. 0 0 b. 0 2 r r r c. 0 2 r r d. 0 2 r r r e. none of the above 4

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Steven A. Jones BIEN 501 Physiological Modeling Midterm Exam April 7, 2004 This question comes from the standard result from differential calculus that: r r f r r f r r f r 0 lim . It is thus necessary to determine what r f looks like. Notice that if one lets r r r f r 2 , and evaluates this expression at r r r and subtracts the expression evaluated at r r , one obtains: 0 ) ( 2 2 r r r r r r r r r Therefore, the correct answer is d. 11. A primary reason for the non-Newtonian properties of blood is: a. The formation of rouleax by the red blood cells. b. The presence of albumen. c. Repulsive forces between red blood cells. d. Dark energy. e. none of the above This question was designed to see if the student was paying attention in class. It was mentioned that the primary reason for the non-Newtonian properties of blood is the formation of rouleaux by the red blood cells. Red blood cells tend to stack on top of one another and stick together when they are under stagnant conditions. Shearing tends to unstuck the cells, thus making it easier to move layers of fluid with respect to one another. The presence of albumen may have some influence, but is minimal in terms of non-Newtonian properties and was never mentioned in the lecture. Repulsive forces between the cells are not important in the context of non-Newtonian viscosity. Dark energy is a concept in astronomy and is not relevant to the question. The correct answer is therefore a. 12. The equation of continuity states that: a. Force is continuous throughout the volume of interest. b. Density is constant throughout a control volume. c. Velocity is zero on any non-moving boundary. 5
Steven A. Jones BIEN 501 Physiological Modeling Midterm Exam April 7, 2004 d. The net amount of matter entering a control volume through the surface is equal to the gain in matter within that volume. e. None of the above. The equation of continuity is a statement that mass is conserved. It does describe forces on the flow, and so answer a is incorrect. It also does not explicitly state that density is constant throughout a control volume. If, however, one adds the assumption of incompressible flow, then the density will be constant, but this is an additional restriction on continuity and therefore not the basis for the continuity equation, so answer b is incorrect. Answer c is also incorrect. The statement that velocity is zero on a non-moving boundary is called the “no-slip” condition, and it is entirely independent of the formulation for the continuity equation.

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