Poiseulle\'s law remains valid as long as the fluid flow is laminar. For suffici

Question

Poiseulle'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 Re is less than about 2000; Re=2vpR/n. Here v, p, and n 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 (p=1060 kg/m^3, n=4*10^-3 Pa*s) could have and still remain in laminar flow when it flows through the aorta. R=1.5*10^-3m

Explanation / Answer

For laminar flow:

2 v R / < 2000

Rearranging gives:

v < 2000 / (2 R)

So the highest will be:

v = 2000 / (2 R)

= (2000 * 4*10^-3) /( 2 * 1060 * 1.5*10^-3)

= 2.52 m/s (ans)

It’s that simple! Hope this helps :)

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