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Re: Bernoulli's relationship



Robert, I characterize your puzzler as posed, mischievous.
I like that in a person!

You were supposing (correctly as it happened) that people would
not recall the possibility of the downstream hydraulic jump.
Here, a supercritical flow ( one running faster than the interfacial
small gravity wave propagation velocity) gives way to a slower
flow in the channel - at a higher level.

It is this possibility that renders the question indeterminate as given.
One may arrange the output level immediately downstream to be lower
or higher than the upstream level. This has the consequence that a
leak may flow either way.

Brian Whatcott

At 18:26 11/8/00 -0500, Robert Cohen wrote:
///
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?
///
| Robert Cohen Department of Physics |
| East Stroudsburg University
brian whatcott <inet@intellisys.net> Altus OK
Eureka!