Question

Blood takes about 1.65 s to pass through a 2.00 mm long capillary. If the diameter of the capillary is 5.00 μm and the pressure drop is 2.85 kPa , calculate the viscosity of blood. Assume laminar flow.

Answer 1

Answer:

Viscosity of blood will be $918.54\times 10^{-6}Pa-sec$

Explanation:

We have given time to pass the capillary = 1.65 sec

Length of capillary L = 2 mm = 0.002 m

Pressure drop $\Delta P=2.85kPa=2.85\times 10^3Pa$

Diameter $d=5\mu m=5\times 10^{-6}m$

So radius $r=\frac{5\times 10^{-6}}{2}=2.5\times 10^{-6}m$

Velocity will be $v=\frac{L}{t}=\frac{0.002}{1.65}=1.212\times 10^{-3}m/sec$

We know that viscosity is given by $\eta =\frac{r^2\Delta P}{8Lv}=\frac{(2.5\times 10^{-6})^2\times 2.85\times 10^3}{8\times 0.002\times 1.212\times 10^{-3}}=918.54\times 10^{-6}Pa-sec$

Viscosity of blood will be $918.54\times 10^{-6}Pa-sec$