What is Reynold's number ? Give its significance.

On the opposite sides of a wide vertical vessel filled with water, two identical holes are opened, each having the cross-sectional area $S=0.50 {\mathrm{cm}}^2$. The height difference between them is equal to $\mathrm{\Delta }h=51 \mathrm{cm}$. Find the resultant force of reaction of the water flowing out of the vessel.

$\left(\text{Gravitational acceleration, }g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\text{ and Density of water }=1000 \mathrm{Kg} {\mathrm{m}}^{-3}\right)$

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. What is the largest average velocity of blood flow in an artery of diameter $2 \times {10}^{-3} \mathrm{m}$ if the flow must remain laminar? (Viscosity of blood, $\mathrm{\eta } = 2.084 \times {10}^3 \mathrm{Pa} \mathrm{s}$, Density of blood, $\mathrm{\rho } = 1.06 \times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$)

Define unsteady flow of liquid.

(a) What is the largest average velocity of blood flow in an artery of radius $2 \times {10}^{-3} \mathrm{m}$ if the flow must remain laminar? (Take density of blood to be $1.06 \times {10}^3 \raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^3$}\right.$)
(b) What is the corresponding flow rate? (Take viscosity of blood to be $2.084 \times {10}^{-3} \mathrm{Pa} \mathrm{s}$).