Does the Movement of Flagella Contradict Bernoulli's Principle?

[Simfish]

http://en.wikipedia.org/wiki/Flagella

So I was reading Purcell's "Life at Low Reynolds Numbers", which I found interesting. So here's a question:

The flagellum help propel the cell forward. The question is - the flagella should increase the velocities of the fluid molecules behind the cell, right? But if it increases the velocities of the fluid molecules behind the cell, shouldn't the pressure gradient be decreasing behind the cell, causing the cell to move backwards? (as we know from http://en.wikipedia.org/wiki/Bernoulli's_principle). Am I missing something?

 

[arildno]

Bernoulli's principle??
You have not an ideal fluid here, i.e, with no friction, nor is the flow stationary.

It is a complete misapplication of Bernoulli's principle.

Furthermore, you have turned this upside down when it comes to the proper use of Bernoulli along a streamline:

The reason why the velocity then is higher at the point of lower pressure is because the fluid element that has traversed the streamline experienced an ACCELERATION due to the existing pressure difference.

If the pressure on the right hand side is greater than on the left-hand side, then the velocity of the element will be the highest on the left-hand side, since it has experienced a pressure force in that direction, causing acceleration.