Question

A small artery has a length of 1.10 × 10-3 m and a radius of 2.50 × 10-5 m. If the pressure drop across the artery is 1.15 kPa, what is the flow rate through the artery? Assume that the temperature is 37°C and the viscosity of whole blood is 2.084 × 10-3 Pa·s.

Answer 1

Answer:

$7.69533\times 10^{-11}\ m^3/s$

Explanation:

P = Pressure difference = 1.15 kPa

r = Radius = $2.5\times 10^{-5}\ m$

$\eta$ = Viscosity of liquid = $2.084\times 10^{-3}\ Pas$

l = Length of artery = $1.1\times 10^{-3}\ m$

From Poiseuille's equation we have

$Q=\frac{\pi Pr^4}{8\eta l}\\\Rightarrow Q=\frac{\pi 1.15\times 10^3\times (2.5\times 10^{-5})^4}{8\times 2.084\times 10^{-3}\times 1.1\times 10^{-3}}\\\Rightarrow Q=7.69533\times 10^{-11}\ m^3/s$

The flow rate of blood is $7.69533\times 10^{-11}\ m^3/s$