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# Blood FlowSuppose a blood vessel has radius R and length /. Let P represent the pressure difference between the ends of the vessel, and let n (eta) represent the vi...

## Question

###### Blood FlowSuppose a blood vessel has radius R and length /. Let P represent the pressure difference between the ends of the vessel, and let n (eta) represent the viscosity of the blood: The velocity of a blood molecule that flows along this vessel depends on how close or far it is from the vessel's central axis. Blood in the center of a vessel flows much faster than blood near a vessel wall. The velocity of a blood molecule positioned at a distance r from the central axis is as follows. Thi

Blood Flow Suppose a blood vessel has radius R and length /. Let P represent the pressure difference between the ends of the vessel, and let n (eta) represent the viscosity of the blood: The velocity of a blood molecule that flows along this vessel depends on how close or far it is from the vessel's central axis. Blood in the center of a vessel flows much faster than blood near a vessel wall. The velocity of a blood molecule positioned at a distance r from the central axis is as follows. This is known as the law of laminar flow: P v(r) = (R2 _r2) 4nl The flux is the volume ofa blood that passes a cross-section per unit of time: This can be found by multiplying the area of a cross-section 2rr by the velocity V, and then by integrating all of this from 0 to R with respect to the variable r. Complete this integration to show that the flux is proportional to the fourth power of the radius of the blood vessel,

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