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 = (VD)/(upsilon)`

Here,

V = Flow Velocity

`\upsilon` = Kinematic viscosity

D = Size of object

For Whale

`Re = (10*30)/(1.83*10^(-6))`

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

For bacterium

`Re = ((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