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

`7.69533* 10^(-11)\ m^3/s`

Step-by-step explanation:

P = Pressure difference = 1.15 kPa

r = Radius =
`2.5* 10^(-5)\ m`

`\eta` = Viscosity of liquid =
`2.084* 10^(-3)\ Pas`

l = Length of artery =
`1.1* 10^(-3)\ m`

From Poiseuille's equation we have

`Q=(\pi Pr^4)/(8\eta l)\\\Rightarrow Q=(\pi 1.15* 10^3* (2.5* 10^(-5))^4)/(8* 2.084* 10^(-3)* 1.1* 10^(-3))\\\Rightarrow Q=7.69533* 10^(-11)\ m^3/s`

The flow rate of blood is
`7.69533* 10^(-11)\ m^3/s`