What is the relation between Bernoulli's principle & Pascal?

  • #1
Bernoulli's principle states that under dynamic conditions total energy inside the fluid container remains constant. and if area is decreases then pressure decrease . and
Pascal states that pressure = force/area . here if area decreases then pressure increase .
I'm getting confusing understanding how it is so?
please clear my problem .........
 

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  • #2
sophiecentaur
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Pascal states that pressure = force/area . here if area decreases then pressure increase .
But that is for a stationary case - pressure from the heel or sole of a high heeled shoe, for instance.
Bernouilli is different. When a fluid is flowing into a narrow pipe section, the velocity has to increase, in order to get the same mass flow rate. That means there must be greater pressure before the constriction to accelerate the fluid.
If you are having trouble with this, then you have to realise that we are dealing with a steady state situation where the flows and pressures have settled down. Bernoilli doesn't say that suddenly inserting a narrow section will cause the pressure inside it to be lower; it says that everything will change. The pressure will end up lower than the pressure upstream. Also, when the constriction opens out to a wide section, the fluid will slow down and that involves a net back pressure, giving a higher pressure downstream than in the narrow section.
 
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  • #3
does the pressure exerted by the fluid on the pipe decreases or is their any other logic behind it?
 
  • #4
sophiecentaur
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“Logic?”
The upstream pressure is higher than in the narrow section. Is that surprising? After all, you are ‘squeezing’ more water into less space.
Remember, the ‘drop’ in pressure is not ‘sucking’ fluid into the narrow part. We are describing the situation as it is after things have settled down.
If you are finding it non-intuitive then apply my argument and be prepared to go against intuition.
Intuition can be horribly wrong sometimes. ;-)
 
  • #6
sophiecentaur
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how p=f/a works here( in narrow section ) ?
That formula is a correct definition of pressure but you have to apply it correctly. With a solid object, the force is set (by the weight of the person, perhaps) and the area is set by the size of the shoe. You can alter the pressure by altering the size of the shoe. (p=F/a)
With a fluid, the static pressure is the same all over and two pistons of different areas, connected to the same fluid container will have the same pressure but different Forces. (F = Pa).
If you block the output of your pipes in the OP, the pressures will have the same values. Only when you start to allow fluid flow will Bernoulli come into play - for the reasons I gave (i.e. you need to accelerate the fluid into the narrow section etc. etc.)
 
  • #8
boneh3ad
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Also, please note that Pascal's law does not say ##p=FA##, and Bernoulli's equation says nothing about areas.

Pascal's law states that a change in pressure in a fluid is transmitted equally to all other parts of the fluid and leads to the development of hydrostatic pressure.

Bernoulli's equation relates pressure, velocity, and height but says nothing about area.

If you want to include area, you have to use the concept of conservation of mass in a flowing fluid.
 

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