Q1. A scientist attempts to model the flow of blood through an artery using a ho

Question

Q1. A scientist attempts to model the flow of blood through an artery using a hollow pipe of diameter 1.8 cm. A fluid of density 1060 kg/m3 is used to simulate blood in the pipe. Viscous effects can be considered to be negligible. (a) If the pipe is held vertical and the fluid is stationary, what would be the difference in pressure between two points along the pipe separated by a height of 450 mm? (b) To study a blockage in an artery, the scientist holds the pipe horizontally and places a constriction in the pipe reducing the diameter to 1.1 cm. What is the speed of the fluid as it passes through the narrowest point of the blockage? Assume that the speed in the unconstricted region is 0.75 m/s (c) For the arrangement described in part (b), calculate the pressure difference between the fluid at the con- striction and the fluid in an unconstricted part of the pipe

Explanation / Answer

a) pressure difference is dP = rho*g*h = 1060*9.81*450*10^-3 = 4679.4 Pa

b) Using equation of continuty

A1*v1 = A2*v2

pi*r1^2*v1 = pi*r2^2*v2

r1^2*v1 = r2^2*v2

1.8^2*0.75 = 1.1^2*v2

v2 = 2 m/sec

C) pressure difference is dP = 0.5*rho*(v2^2-v1^2)

dP = 0.5*1060*(2^2-0.75^2)

dP = 1821.875 Pa

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