Question

Calculate the Reynolds number of a whale (30 m) swimming in seawater (ν = 1.83 × 10-6 m2 /s) at 10 m/s; the Reynolds number of a bacterium (2 µm) in blood (ν = 2.65 × 10-6 m2 /s) at 15 µm/s. Which one is dominated by viscosity and which by inertia? Check you units!

Answer 1

The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities, which is known as a boundary layer in the case of a bounding surface such as the interior of a pipe. Reynolds number is given by,

$Re = \frac{VD}{upsilon}$

Here,

V = Flow Velocity

$\upsilon$ = Kinematic viscosity

D = Size of object

For Whale

$Re = \frac{10*30}{1.83*10^{-6}}$

$Re = 1.64*10^8 \rightarrow Re >1$

For bacterium

$Re = \frac{(15*10^{-6})(2*10^{-6})}{2.65*10^{-6}}$

$Re = 11.32*10^{-6} \rightarrow Re<1$

$\therefore$ Bacteria lives in the world where viscosity is dominated