   Chapter 12, Problem 60PE

Chapter
Section
Textbook Problem

Assuming that blood is an ideal fluid, calculate the critical flow rate at which turbulence is a certainty in the aorta. Take the diameter of the aorta to be 2.50 cm. (Turbulence will actually occur at lower average flow rates, because blood is not an ideal fluid. Furthermore, since blood flow pulses, turbulence may occur during only the high-velocity part of each heartbeat.)

To determine

To calculate the critical flow rate of blood.

Explanation

Given:

Diameter d= 2.50 cm = 0.025 m

Radius r=0.025 m2=  1.25 × 102m

Density of blood ρ= 1050 kg/m3

Coefficient of viscosity η= 2.084 × 103Ns/m2

As the flow is turbulent, we take Reynolds number Re= 3000

Formula used:

Re=2ρvrη where v=Qπr2 and Qis the critical flow rate

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