(a) What is the largest average velocity of blood flow in an artery of radius `2 xx 10^-3` m if the flow must remain laminar? (b) What is the corresponding flow rate? (Taking viscosity of blood to be `2.084 xx 10^-3 Pa s)`

Explanation

We are given: `r=2xx10^(-3)m`
`eta=2.084xx10^(-3)` Pa s.
We are to calculate: maximum velocity and rate of flow
We know that, Maximum value of Reynold number for streamline flow as `R_(e)=2000`.
Using relation : `R=(rhovd)/(eta)`
`v_(c)=(R_(e)eta)/(rhod)=(R_(e)eta)/(2rhor)=(2000xx2.084xx10^(-3))/(2xx1060xx2xx10^(-3))=0.98m//s`
Also, rate of flow is `v_(c)=(R_(e)eta)/(rhod)=(R_(e)eta)/(2rhor)=(2000xx2.084xx10^(-3))/(2xx1060xx2xx10^(-3))=0.98m//s`