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Marina CMI [18]
3 years ago
10

Poiseuille's law remains valid as long as the fluid flow is laminar. For sufficiently high speed, however, the flow becomes turb

ulent, 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 = 2v Normal 0 false false false IN X-NONE X-NONE MicrosoftInternetExplorer4 rhoR Normal 0 false false false IN X-NONE X-NONE MicrosoftInternetExplorer4 /η. Here Normal 0 false false false IN X-NONE X-NONE MicrosoftInternetExplorer4 v, rho, and η are, respectively, the average speed, density, and viscosity of fluid, and R is the radius of the pipe. Calculate the highest average speed that blood (rho = 1060 kg/m3, η = 4.0 x 10-3 Pa.s) could have and still remain in laminar flow when it flows through the aorta (R = 8.0 x 10-3 m)
Normal 0 false false false IN X-NONE X-NONE MicrosoftInternetExplorer4
Physics
1 answer:
Ilia_Sergeevich [38]3 years ago
4 0

Answer: 0.471 m/s

Explanation:

We are given the followin equation:

Re=\frac{D v \rho}{\eta} (1)

Where:

Re is the Reynolds Number, which is adimensional and indicates if the flow is laminar or turbulent

When Re we have a laminar flow

When Re>4000 we have a turbulent flow

When 2100 the flow is in the transition region

D=2R is the diameter of the pipe. If the pipe ha a radius R=8(10)^{-3} m its diameter is D=2(8(10)^{-3} m)=0.016 m

v is the average speed of the fluid

\rho=1060 kg/m^{3} is the density of the fluid

\eta=4(10)^{-3} Pa.s is the viscosity of the fluid

Isolating v:

v=\frac{Re \eta}{D \rho} (2)

Solving for Re=2000

v=\frac{(2000)(4(10)^{-3} Pa.s)}{(0.016 m)(1060 kg/m^{3})} (3)

Finally:

v=0.471 m/s

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