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Bernoulli's relationship



I hate to bring up a topic with so much phys-l historical baggage, but I
have run into a question with fluids. Rather than explain my problem, I
put forth the following question. Perhaps someone can answer it. It
seems rather straightforward but I am having difficulty answering it.

Suppose you have an infinitely-long W-shaped canal:

| | |
|^^^^^^^^|^^^^^^^^^|
| | |
| | |
| | |
| | |
--------------------

Each trough contains the same amount of water.

In one trough, there is a propeller pushing the water down the trough.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
//
//
// motion of water
// --------->
//
//
-----------------------------------------
^
/|\
|
|
|
location of propeller

1. With the propeller on, what does the surface of the water look like in
that trough? In other words, where along the trough is the surface of the
water raised above or below the surface of water in the stationary trough?

2. How does the water pressure (at some level) inside the moving trough
vary with distance along the trough (and how does it compare to the
pressure at the same height in the stationary trough)? I assume this is
related to the height of the water along the trough.

3. If at some point, there is a hole in the boundary between the two
troughs, into which trough would the water flow and why?

P.S. My intention is not to get into a debate on whether a difference in
fluid speeds causes a pressure difference (the popular "explanation" for
why a plane flies) or visa-versa (the popular "a force must cause an
acceleration" argument). Use whichever you wish and I'll try to interpret
your answer within that construct.

----------------------------------------------------------
| Robert Cohen Department of Physics |
| East Stroudsburg University |
| bbq@esu.edu East Stroudsburg, PA 18301 |
| http://www.esu.edu/~bbq/ (570) 422-3428 |
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