Question

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 37°C.)

(a) ( 2.52 × 10⁻⁶ , {m}³/{s} )
(b) ( 4.16 × 10⁻⁶ , {m}³/{s} )
(c) ( 6.62 × 10⁻⁶ , {m}³/{s} )
(d) ( 1.03 × 10⁻⁵ , {m}³/{s} )

Answer 1

The flow rate through the artery can be calculated using Poiseuille's law, which takes into account the pressure drop, radius, viscosity, and length of the artery. Substituting the given values into the formula, we can find the flow rate as 6.62 × 10⁻⁶ m³/s.

Step-by-step explanation:

The flow rate through an artery can be determined using Poiseuille's law, which states that the flow rate is directly proportional to the pressure drop and the fourth power of the radius, and inversely proportional to the viscosity and length of the artery. The formula for flow rate is given by:

Q = (ΔP * π * r4) / (8 * η * L)

where Q is the flow rate, ΔP is the pressure drop, r is the radius, η is the viscosity, and L is the length of the artery.

Using the given values, the flow rate through the artery can be calculated as:

Q = (1.3 * 10^3 * π * (2.5 * 10^-5)^4) / (8 * η * 1.1 * 10^-3)

After evaluating the expression, we get the flow rate as 6.62 × 10⁻⁶ m³/s, which matches option (c).