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The radial artery in a person has an inner diameter of 4 mm and is 25 cm long. The viscosity of blood is 3×10−33×10−3 Pa•s, and its density is 1.055 g cm−31.055g cm−3. A pascal is one N m−2−2. Using this information, answer the following questions:

1. Calculate the flow rate of blood through the radial artery.
2. Determine the Reynolds number for the blood flow in the radial artery.
3. Assess whether the flow is likely to be laminar or turbulent based on the Reynolds number.
4. Calculate the resistance to flow in the radial artery.

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Final answer:

The flow rate of blood through a radial artery is calculated using the Hagen-Poiseuille equation based on the artery's dimensions, pressure drop, and blood viscosity. The Reynolds number determines the nature of the blood flow, indicating whether it is laminar or turbulent. Resistance to blood flow is derived from the pressure drop and flow rate.

Step-by-step explanation:

To determine the flow rate and assess whether the flow is laminar or turbulent in a radial artery, one must apply principles from fluid dynamics. In a typical scenario with given pressure drops, artery dimensions, viscosity, and density of blood, calculations such as the Reynolds number and flow rate using the Hagen-Poiseuille equation can be conducted.

For instance, to calculate the flow rate (Q) through a cylindrical vessel like an artery, one would use the equation:

Q = (πΔPr^4) / (8ηL)

Where ΔP is the pressure drop, r is the radius of the artery, η is the dynamic viscosity of the blood, and L is the length of the artery.

Furthermore, the Reynolds number (Re) is calculated to determine the nature of flow:

Re = (ρvd) / η

Where ρ is the density of blood, v is the mean velocity of blood flow, and d is the diameter of the artery.

Generally, if Re < 2000, the flow is considered to be laminar; if Re > 4000, the flow is likely to be turbulent. In the intermediate range, the flow could be transitioning from laminar to turbulent.

The resistance to flow in the artery can be found using the equation R = ΔP/Q, which stems from Ohm's Law analog for fluids.

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