A device known as pulse oximeter is used to record the variation in blood volume in superficial blood vessels due to the cardiac cycle (heart rate). To consider the blood flow in this situation, we would need to extend our blood flow model to three dimensions. The continuity equation (conservation of mass) still applies and is formulated in 3D as др + V • (pū) = 0, at %3D where p(x, y, z, t) is the density of the fluid, ū = (u, v,w) is the 3D velocity vector, and the rates of dx change with time of the three spatial dimensions x, y, z “following the fluid" are dt dy = U. dt = v, dz = w. dt 2.1. Prove that the divergence of the velocity of this 3D flow is equal to 0 if the fluid is incompressible (which means the total derivative of the density p with respect to time "following the fluid" is equal 0). 2.2. The acceleration of a fluid element in 3D is given by: ди + (ū · A)ū. at Find the acceleration of this fluid element if the fluid is undergoing uniform rotation such that u = (-wy, wx, 0) and the flow vector with respect to time is 0). known to be steady (the rate of change of the velocity

A device known as pulse oximeter is used to record the variation in blood volume in superficial blood vessels due to the cardiac cycle (heart rate). To consider the blood flow in this situation, we would need to extend our blood flow model to three dimensions. The continuity equation (conservation of mass) still applies and is formulated in 3D as др + V • (pū) = 0, at %3D where p(x, y, z, t) is the density of the fluid, ū = (u, v,w) is the 3D velocity vector, and the rates of dx change with time of the three spatial dimensions x, y, z “following the fluid" are dt dy = U. dt = v, dz = w. dt 2.1. Prove that the divergence of the velocity of this 3D flow is equal to 0 if the fluid is incompressible (which means the total derivative of the density p with respect to time "following the fluid" is equal 0). 2.2. The acceleration of a fluid element in 3D is given by: ди + (ū · A)ū. at Find the acceleration of this fluid element if the fluid is undergoing uniform rotation such that u = (-wy, wx, 0) and the flow vector with respect to time is 0). known to be steady (the rate of change of the velocity

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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