File Edit View Sign Window Help Home Tools MATH_124.pdf X 2 12 100% - Problem 3: Blood Flow As discussed in Project 1, we can model the shape of the blood vessels by a cylindrical tube with radius R and length I as shown in the figure below. T represents the distance from the central axis. 1 1 The relationship between v and r is given by the law of laminar flow U = (R2 -12 ) where the constants are R (radius of the blood vessel), / (viscosity of the blood), I (length), and P (pressure difference between the ends of the tube). The average value of a function f on the interval [a, b] is given by the formula (a) Find the average velocity (with respect to r) over the interval Or $ R. (b) Is the value from (a) equal to the average between the maximum and minimum velocities ( determine these quantities) on the interval 0. R]? How can this behaviour be justified using the second derivative of u(r)? (c) The flux for discharge) is the volume of the blood that passes a cross-section per unit time and is2 12 100% The relationship between v and r is given by the law of laminar flow P U = Aut ( R" - 72 ) where the constants are R (radius of the blood vessel), a (viscosity of the blood), I (length), and P (pressure difference between the ends of the tube). The average value of a function f on the interval [a, b] is given by the formula (a) Find the average velocity (with respect to r) over the interval 0 ST