Question

In which case does viscosity play a dominant role? Case A: a typical bacterium (size ~ 1 mm1 mm and velocity ~ 20 mm/s20 mm/s) in fresh water. Case B: a swimmer (size ~ 1.5 m1.5 m and velocity ~ 3 m/s3 m/s) in fresh water. Or same for both?

Answer 1

Answer:

Case A

Explanation:

given,

size of bacteria = 1 mm x 1 mm

velocity = 20 mm/s

size of the swimmer = 1.5 m x 1.5 m

velocity of swimmer = 3 m/s

Viscous force

$F = \eta A \dfrac{dv}{dx}$

for the bacteria

$F = \eta \times 10^{-6}\times 20\times 10^{-3}$

$F =2\times 10^{-8} \eta\ N$

for the swimmer

$F = \eta \times 1.5^2\times 3$

$F =6.75 \eta\ N$

from the above force calculation

In case B inertial force that represent mass is more than the inertial force in case of bacteria.

Viscous force is dominant in case of bacteria.

So, In Case A viscous force will be dominant.