Poiseuilles\' law remains valid as long as the fluid flow is laminar. For suffic
ID: 1699925 • Letter: P
Question
Poiseuilles' 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 2200.Re = 2 v?R / ?
Here v, ?, and ? 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 (? = 1060 kg/m3, ? = 4.00 10-3 Pa · s) could have and still remain in laminar flow when it flows through the aorta (R = 7.20 10-3 m).
m/s
Explanation / Answer
The Reynold number is given by the equation
Re = 2vR/
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
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 = Remax/2R
vmax = (2200)(4.00 10-3)/2(1060)(7.20 10-3)
vmax = 0.5765 m/s