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.

(N/A) Given:
Diameter of the artery,$d = 2 \times 10^{-3} \; m$
Viscosity of blood,$\eta = 2.084 \times 10^{-3} \; Pa \cdot s$
Density of blood,$\rho = 1.06 \times 10^{3} \; kg/m^3$
Reynolds' number for laminar flow,$N_{R} = 2000$
$(a)$ The largest average velocity $(V_{avg})$ for laminar flow is given by the formula:
$V_{avg} = \frac{N_{R} \eta}{\rho d}$
Substituting the values:
$V_{avg} = \frac{2000 \times 2.084 \times 10^{-3}}{1.06 \times 10^{3} \times 2 \times 10^{-3}}$
$V_{avg} = \frac{4.168}{2.12} \approx 1.966 \; m/s$
$(b)$ Yes,the dissipative forces become more important as the fluid velocity increases. This is because higher velocities lead to the onset of turbulence. In turbulent flow,the fluid particles move in irregular paths,leading to increased internal friction and energy dissipation compared to laminar flow.