Question

Biophysics

What is the Reynolds number of a swimming bacterium? A swimming tadpole? A swimming blue whale? (assume in water with density of 1 g/cm^3 and viscosity of 10^-3 Pa-sec)

Answer 1

Hey there!

The formula for Reynold's number can be given as

where,

- density of the liquid (1 gm / cm³ = 1kg / m³)

V - Velocity at which the organism travels

L - Length of the organism

- Viscosity of the liquid (10^-3 Pa s).

If Re < 2000, the flow is called Laminar and if Re > 4000, the flow is called turbulent and If 2000 < Re < 4000, the flow is called transition.

Let us solve for each case now.

The length (L) of the bacterium can be taken to be 0.001 mm or 0.1 x 10^-6 m. The velocity (V) at which the bacterium moves to be at 0.05 mm / s . = 5 x 10^-5 m/s.

FOR A SWIMMING TADPOLE

Let us consider the length of the tadpole to be L = 3 cm = 0.03 m and the velocity at which the tadpole travels to be 0.3 m /s (assumption on an average value). Hence the Reynold's number is

FOR A SWIMMING WHALE

Let us consider the length of the whale to be L = 25 m and the velocity at which the tadpole travels to be 25 km / hr = 7 m /s (assumption on an average value). Hence the Reynold's number is

I hope the solution helps... Feel free to comment and discuss further... Cheers :)