Yuri B. said:
What I meant rather asking my qwestion :
Can SP be lower upstreem of a point in a closed system consisting of the pipes of different diameters (and no phase change - only incompressible liquid)?
Sure - let's neglect friction and look at venturi effect. That's the most direct application of Bernoulli.
Where velocity is higher dynamic pressure is higher because it's \frac{1}{2}V
2.
Total pressure is sum of dynamic and static pressures and is constant.
Bernouli says we can swap between dynamic and static pressures.
So in larger parts of your pipe the static pressure will be higher and the dynamic pressure lower than in the smaller parts. But their sum will be constant.
A picture of a venturi courtesy of these guys:
http://www.lenntech.com/venturi.htm
Observe lower static pressure in mid section, which is upstream of right section.
I think that was your question.
Would not that imply the possibility of the existence of such thing as "negative P drop" ?!
Those words don't sound right to me but it may be a language barrier - I'm old and don't adapt as quick as I used to.
I prefer to think of it this way:
Imagine a tiny cube of water drifting along in that stream above.
If you wish, imagine yourself very tiny and inside that very cube of water wearing a diver's suit.
In order for the flowing stream to pass into the narrow part of the tube it MUST speed up.
That's because the area for flow is smaller.
You see this every day in any river - water moves fast in shallow rapids and slow where the stream is deep.
Now - in order for any mass to speed up it must receive a lateral force.
So your tiny cube of water must see more pressure on its backside than it does on its front side. Else it wouldn't accelerate.
So where it is accelerating, namely in the converging part of the venturi(where it's narrowing), pressure
must be decreasing. Else the water could not accelerate for there'd be no lateral force.
Go over that until it makes sense...In the narrow part of the venturi pressure is constant as evidenced by fact the water is neither accelerating nor decelerating.
In the diverging(widening) part of the venturi water is slowing down(decelerating) so it MUST be feeling more pressure from downstream side than upstream.
So pressure in that section is
increasing.
With no friction the pressure would come back to same as upstream, in a real venturi it can come very close(better than 99% for a high quality metering venturi).
That imaginary model is what made Bernoulli "click" for me - the fact water can't change velocity without a push.
Some people like me have to see a physical model before we can accept an equation.*
I hope this helps you believe in Bernoulli's principle - it is really useful.
You see it in practical application everywhere.
Those sprayers for your garden hose use a venturi to suck the spray into the water stream
Those drainers for waterbeds use a venturi to suck the water out of the mattress
Every carburetor you'll likely encounter uses a venturi to suck the fuel into the airstream.
(* I read somewhere that this inability to accept pure math without a physical model is characteristic of English speaking people. There are some interesting papers(e.g. Richard Restrak) on how one's native language seems to determine what areas of the brain are used in problem solving - but that's another whole subject.
I mention it only to assure you my earlier remark about language barrier is not in any way a criticism, unless it's of myself.)
Good luck, friends
old jim
