What is the Reynolds number for blood leaving the heart through the aorta if the diameter of the aorta is 2.15 cm, and the blood has a dynamic viscosity of 2.70×10−3 Pa · s, a density of 1050 kg/m3, and travels at a mean fluid velocity of 31.7 cm/s?
To calculate the Reynolds number, we need the formula:
Re = (ρ * v * D) / μ
where:
Re = Reynolds number
ρ = density of the fluid
v = mean fluid velocity
D = characteristic length (in this case, the diameter of the aorta)
μ = dynamic viscosity of the fluid
Given:
Diameter of the aorta (D) = 2.15 cm = 0.0215 m
Dynamic viscosity (μ) = 2.70 × 10^(-3) Pa · s
Density (ρ) = 1050 kg/m^3
Mean fluid velocity (v) = 31.7 cm/s = 0.317 m/s
We can substitute these values into the Reynolds number formula:
Re = (ρ * v * D) / μ
Re = (1050 kg/m^3 * 0.317 m/s * 0.0215 m) / (2.70 × 10^(-3) Pa · s)
Now we can solve this equation to find the Reynolds number.