Question

What is the reynolds number re 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 x 10⁻³ pa, a density of 1050 kg/m³ and travels at a mean fluid velocity of 29.7 cm/s?

Answer 1

The Reynolds number for blood leaving the heart through the aorta is approximately 22,300, calculated using the formula Re = (ρvD) / μ with the given blood properties and aortic dimensions.

Step-by-step explanation:

The Reynolds number (Re) provides insight into the flow regime of a fluid through a pipe or blood through an artery. It is a dimensionless number that is calculated by multiplying the fluid's density (ρ) by its velocity (v) and the diameter of the pipe (D), and then dividing the product by the fluid's dynamic viscosity (μ).

To calculate the Reynolds number for blood leaving the heart through the aorta, we use the given value

The formula for Reynolds number is:

Re = (ρvD) / μ

Substituting the values:

Re = (1050 kg/m³) * (0.297 m/s) * (0.0215 m) / (2.70 x 10⁻³ Pa·s)

Performing the calculation gives us Re = 2.23 x 10⁵.

Thus, the Reynolds number for blood leaving the heart through the aorta under these conditions is approximately 22,300.