What is the largest average velocity of blood flow in an artery of radius `2xx10^(-3)m` if the flow must remain laminar > (b) What is the corresponding flow rate ? (Take vicosity of blood to be `2.084xx10^(-3)`Pa s).

Explanation

Density of blood `rho=1.06xx10^(3)kgm^(-3)`
Radius of the artery `r=2xx10^(-3)`
The coefficient of viscosity of blood,
`eta=2.84xx10^(-3)`Pas
For streamline flow `N_(R)=2000`
(a) Suppose the largest average velocity of blood is v,
Reynold.s number
`R_(e)=(RhovD)/(eta)`
`thereforev=(R_(e)eta)/(rgoD)`
`(2000xx2.084xx10^(-3))/(1.06xx10^(3)xx2xx2xx10^(-3))`
`=983xx10^(-3)`
`=0.983`
`thereforev=0.98ms^(-1)`
(b) Suppose flow ate of blood is V,
`thereforeV=` arrea of cross section of artery `xx` velocity of blood
`=pir^(2)xxv`
`=3.14xx(2xx10^(-3))^(2)xx0.98`
`=12.3xx10^(-6)`
`=1.23xx10^(-5)m^(3)s^(-1)`