Physics@Brock

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Poiseuille's law remains valid as long as the fluid flow is laminar. For sufficiently high speed, however, the flow becomes turbulent, even if the fluid is moving through a smooth pipe with no restrictions. It is found experimentally that the flow is laminar as long as the Reynolds number ${\cal R}$ is less than about 2000: $$ {\cal R} = \frac{2 v \rho r}{\eta}. $$ Here $v$, $\rho$, and $\eta$ are, respectively, the average speed, density, and viscosity of the fluid, and $r$ is the radius of the pipe. Calculate the highest average speed that blood ($ \rho = 1060 \mbox{ kg/m}^3$ could have and still remain in laminar flow when it flows through the aorta ($ r = 8.0 \times 10^{-3}\mbox{ m}$).