Poiseuille\'s law remains valid as long as the fluid flow is laminar. For suffic
ID: 1971047 • Letter: P
Question
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 Re is less than about 2000: Re = 2v Normal 0 false false false IN X-NONE X-NONE MicrosoftInternetExplorer4 R Normal 0 false false false IN X-NONE X-NONE MicrosoftInternetExplorer4 /. Here Normal 0 false false false IN X-NONE X-NONE MicrosoftInternetExplorer4 v, , and 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 ( = 1060 kg/m3, = 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)
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Explanation / Answer
More precise answer is
The Reynold number is given by the equation
Re = 2vR/n
Where v is the average speed of flow
is the dencity of the fluid = 1060 kg/m3
R is the radius of the pipe = 7.20 10-3 m
n is the coefficient of viscocity = 4.00 10-3 Pa · s
The maximum value of Renold number for the flow to be laminar is Remax = 2200
The maximum velocity for the fluid to be in laminar flow is
vmax = Remaxn/2R
vmax = (2200)(4.00 10-3)/2(1060)(7.20 10-3)
vmax = 0.5765 m/s