Final answer:
The Reynolds number for blood leaving the heart through the aorta, given a diameter of 2.15 cm, a dynamic viscosity of 2.70 x 10^-3 Pa·s, a density of 1050 kg/m3, and a fluid velocity of 29.7 cm/s, is approximately 2,467.716. This value indicates that the flow is laminar, but close to the threshold for becoming turbulent.
Step-by-step explanation:
The Reynolds number (Re) is a dimensionless quantity in fluid mechanics that helps to predict flow patterns in different fluid flows. It is used to identify the type of flow, whether it will be laminar or turbulent flow, based on the characteristics of the fluid and the flow conditions. To calculate the Reynolds number for blood leaving the heart through the aorta, we use the formula:
Re = (Density of blood * Velocity of blood * Diameter of aorta) / (Dynamic viscosity of blood)
Given the following values:
- Diameter of aorta = 2.15 cm (0.0215 meters)
- Dynamic viscosity of blood = 2.70 x 10-3 Pa·s
- Density of blood = 1050 kg/m3
- Mean fluid velocity = 29.7 cm/s (0.297 meters/second)
Substituting these into the formula:
Re = (1050 kg/m3 * 0.297 m/s * 0.0215 m) / 2.70 x 10-3 Pa·s
Calculating this gives:
Re = (0.297 * 0.0215 * 1050) / 2.70 x 10-3
Re = 0.0063465 * 1050 / 2.70 x 10-3
Re = 6.663825 / 2.70 x 10-3
Re = 2,467.716 approximately
The Reynolds number for the blood leaving the heart through the aorta is approximately 2,467.716, which typically suggests that the flow is laminar, but nearing the transitional range to turbulent flow.