The most important difference between bacteria and everyday propulsion is size. Bacteria are microscopic.
There are two sources of resistance when moving through water. First, flowing water generates friction forces. These are called viscosity. Second, a moving object must push water out of its way. The reaction forces push the object back. These are called inertial forces.
In most cases, one of these is so much bigger that you might as well ignore the other.
Inertial forces are big when the object is big. Lots of water gets pushed around. Also when the projectile is fast, water must move fast and a larger acceleration is needed to get it out of the way. When the fluid is dense, mass goes up, and so do the forces.
Viscous forces are big when the fluid has more internal friction. Forces are bigger when moving through honey than water.
Viscous forces are more important when the object is small. Most of the fluid motion takes place near the object. Far away, the fluid is not disturbed. There is a layer right next to the object that moves with the object. Just above this, there is a layer that moves a little slower. Just above that, a little slower still. The thickness of the moving region depends on the viscosity. Fluids with a lot of friction drag more fluid with them. For a small object, the layer might be as big as the object. For a microscopic one, it might be bigger.
The ration of inertial forces to viscous forces is called the Reynolds number. While it is difficult to calculate exactly, it is easy to approximate. And an approximation is all you need when one force is overwhelmingly bigger than the other.
$$Re = \frac{\rho uL}{\mu}$$
where
- $\rho$ is the density of the fluid
- $u$ is the velocity
- $L$ is the size of the projectile
- $\mu$ is the viscosity of the fluid
We can plug in a few numbers. See Speed of a Bacterium
$$Re = \frac{(10^6 kg/m^3)(50 \cdot 10^{-6} m/s)(0.5 \cdot 10^{-6} m)}{(10^{-3} kg/{ms})} = 0.025$$
Viscous forces are 40 time bigger.
A ship's propeller pushes large volumes of water backward, creating a large inertial force forward. A bacterium must do something different.
You might think of a flagellum as closer to the threads on a screw, pushing the bacterium forward through a fluid that flows much less than you would expect.
