Question

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 of diameter $2\times {10}^{–3}$ m if the flow must remain laminar? (b) Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.

Answer 1

(a) Diameter of the artery, $d=2\times {10}^{–3}m$
Viscosity of blood,$\eta =2.084\times {10}^{-3}Pas$
Density of blood, $\rho =1.06\times {10}^{3}kg/m^3$
Reynolds’ number for laminar flow, $N_R=2000$
The largest average velocity of blood is given as:
$V_{arg}=\frac{N_R\eta }{\rho d}=\frac{2000\times 2.084\times {10}^{-3}}{1.06\times {10}^3\times 2\times {10}^{-3}}=1.966m/s$
Therefore, the largest average velocity of blood is 1.966 m/s.
(b) Yes, as the fluid velocity increases, the dissipative forces become more important. This is because of the rise of turbulence. Turbulent flow causes dissipative loss in a fluid.