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A small artery has a length of 1.1×10−3m and a radius of 2.5×10−5m. If the pressure drop across the artery is 1.3 kPa, what is the flow rate through the artery? (Assume that the temperature is 37º C.)

A) 1.18 × 10^(-6) m³/s
B) 2.36 × 10^(-6) m³/s
C) 3.54 × 10^(-6) m³/s
D) 4.72 × 10^(-6) m³/s

User Ed Harrod
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1 Answer

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Final answer:

Using Poiseuille's law with an assumed viscosity for human blood at body temperature, the flow rate through the given small artery can be calculated to be approximately 1.18 × 10⁻⁶ m³/s.

Step-by-step explanation:

The flow rate through an artery can be calculated using Poiseuille's law, which states that the flow rate Q through a cylindrical vessel is proportional to the fourth power of the radius of the vessel, the pressure difference ΔP across the vessel, and inversely proportional to the viscosity η and the length L of the vessel. The formula for laminar flow through a cylinder is given by:


Q = π × r4 × ΔP / (8 × η × L)


However, we must take into account that we do not have the viscosity given in the problem statement. Assuming blood behaves like water at body temperature and leveraging a typical value for human blood near 37°C (3.6 × 10-3 Pa·s), we can substitute this into our equation to calculate the flow rate:

Q = π × (2.5 x 10-5 m)4 × (1.3 x 103 Pa) / (8 × 3.6 x 10-3 Pa·s × 1.1 x 10-3 m)

After calculating, we find that the flow rate is approximately:

Q ≈ 1.18 x 10-6 m3/s

Therefore, the correct answer is A) 1.18 × 10-6 m3/s.

User Matvei Nazaruk
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