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.

Respuesta :

Answer:

[tex]7.69533\times 10^{-11}\ m^3/s[/tex]

Explanation:

P = Pressure difference = 1.15 kPa

r = Radius = [tex]2.5\times 10^{-5}\ m[/tex]

[tex]\eta[/tex] = Viscosity of liquid = [tex]2.084\times 10^{-3}\ Pas[/tex]

l = Length of artery = [tex]1.1\times 10^{-3}\ m[/tex]

From Poiseuille's equation we have

[tex]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[/tex]

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