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The Reynolds number, Re, is a dimensionless number used to characterize different flow regimes in a fluid. The Reynolds number can be defined as DVD Re= where D is the diameter of the pipe, V is the mean fluid velocity, p is the density of the fluid, and p is the dynamic viscosity of the fluid. What is the Reynolds number of blood leaving the heart through the aorta if it has a dynamic viscosity of y= 3.70 CP (centipoise), a density of p = 1051 kg/m, travels at a mean fluid velocity of V = 34.3 cm/s, and the diameter of the aorta is D = 2.15 cm?

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daigz92

Answer:

Re=2094,76

Explanation:

For a fluid that circulates inside a straight circular pipe, the Reynolds number is given by:

[tex]Re=\frac{pvD}{u}[/tex]

where (using the international measurement system):

  • ρ: density of the fluid [kg/m3]
  • v: velocity of the fluid [m/s]
  • D: diameter of the pipe through which the fluid circulates [m]
  • μ: dynamic viscosity [Pa.s]

To solve the probelm, we just need to replace our data using THE CORRECT UNITS in the Reynolds number equation. So we have:

ρ=1051 kg/m3,

v=34,3 cm/s=0,343 m/s

D=2,15 cm = 0,0215 m

μ = 3,7 cp * 10^-3 Pa.s/1 cp = 3,7*10^-3 Pa.s

Replacing in the main equation:

[tex]Re=\frac{1051\frac{kg}{m^{3} }*0,343\frac{m}{s}*0,0215m  }{3,7*10^{-3}Pa.s } =2094,76[/tex]

So the Reynolds number is 2094,76 (note that the Reynolds number is a dimensionless quantity).

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