**Reynolds Number for Blood Flow in the Aorta****Problem Statement:**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 \( 2.70 \times 10^{-3} \) Pa·s, a density of 1050 kg/m\(^3\), and travels at a mean fluid velocity of 31.1 cm/s?\( Re = \) [____]**Question:**The blood flow through the aorta in the given scenario is:- \( \bigcirc \) turbulent.- \( \bigcirc \) transitioning between laminar and turbulent.- \( \bigcirc \) laminar.### Explanation:The task is to calculate the Reynolds number, a dimensionless number that helps predict flow patterns in different fluid flow situations. It considers factors such as the fluid's velocity, characteristic length (diameter in this case), fluid density, and viscosity.Understanding the result:- If \( Re \) is less than 2000, the flow is typically laminar.- If \( Re \) is between 2000 and 4000, the flow is in transition.- If \( Re \) is greater than 4000, the flow is generally considered turbulent.This calculation is crucial in fields like biomedical engineering to understand how blood behaves under various physiological conditions.

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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× 10-3 Pa-s, a density of 1050 kg/m³, and travels at a mean fluid velocity of 31.1 cm/s?

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× 10-3 Pa-s, a density of 1050 kg/m³, and travels at a mean fluid velocity of 31.1 cm/s?

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Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.

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**Reynolds Number for Blood Flow in the Aorta**

**Problem Statement:**
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 \( 2.70 \times 10^{-3} \) Pa·s, a density of 1050 kg/m\(^3\), and travels at a mean fluid velocity of 31.1 cm/s?

\( Re = \) [____]

**Question:**
The blood flow through the aorta in the given scenario is:
- \( \bigcirc \) turbulent.
- \( \bigcirc \) transitioning between laminar and turbulent.
- \( \bigcirc \) laminar.

### Explanation:
The task is to calculate the Reynolds number, a dimensionless number that helps predict flow patterns in different fluid flow situations. It considers factors such as the fluid's velocity, characteristic length (diameter in this case), fluid density, and viscosity.

Understanding the result:
- If \( Re \) is less than 2000, the flow is typically laminar.
- If \( Re \) is between 2000 and 4000, the flow is in transition.
- If \( Re \) is greater than 4000, the flow is generally considered turbulent.

This calculation is crucial in fields like biomedical engineering to understand how blood behaves under various physiological conditions.

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