In deriving Bernoulli's equation , we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery ofdiameter 2xx10^(-3)m ifthe flow must remain laminar ? (b)Do thedissipative forcebecome more important as the fluid velocity increases ?Discuss quanlitatively .

In deriving Bernoulli's equation , we equated the work done on the flu

1.	In deriving Bernoulli's equation , we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery ofdiameter 2xx10^(-3)m ifthe flow must remain laminar ? (b)Do thedissipative forcebecome more important as the fluid velocity increases ?Discuss quanlitatively .
Answer» Solution :Diameter of artery `d=2XX10^(-3)m` The coefficient of viscosity of blood `eta=2.084xx10^(-3)`PaS Density of blood `rho=1.06xx10^(3)kg//m^(3)` SUPPOSE , Reynold.s numberfor LINEAR flow , `R_(e)=2000` Maximum average velocityof blood, `v_("avg")=(R_(e)eta)/(rhoD)=(2000xx2.084)/(1.06xx10^(3)xx4xx10^(-3))` `=0.98m//s` (b)Volume of fluid passing per second, `Q=av_("arg")` `=(pi^(r2))v_("avg")` `=(22)/(7)xx(2xx10^(-3))^(2)xx0.98` `=1.23xx10^(-5)m^(3)s^(-1)` As per fluidvelocity increases , the dissipative forces become more important . This is because of the rise of turbulence . Turbulent flow causes dissipative loss in a fluid.