Question

In deriving Bernoullis 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, $D=2\times {10}^{-3}m$

Viscosity of the blood $\eta =2.084\times {10}^{3}Pa$

Density of the blood $\rho =1.06\times {10}^{3}kg{m}^{-3}$

Maximum value of Reynolds number of flow to be laminar, $N_R=2000$

Average velocity $V_c=\frac{N_R\eta }{\rho D}$

$=\frac{2000\times 2.084\times {10}^3}{1.06\times {10}^3\times 2\times {10}^3}$

$=\frac{4.168}{2.12}=1.96m/s$

(b) The dissipative forces become more important with increasing flow velocity, because of turbulence.