# Bernoulli equation

#### ahmedbadr

well,i ve some problems with bernouuli equation.first,i'd like to ask abt meaning of static pressure in flowing fluid because i really ve read abt that in references and many websites but still cant get exactly whats meaningt of static pressure in flowing fluid.

i ve read on website that it's the pressure which exerted on plane parrallel to the flow while another website says static pressure in flowing fluid has direction normal to the flow.also before in reference that pressure ius scalal quantity (no direction) which means its equal on any point in all directions.

that was my 1st question ,my 2nd question abt what makes this static pressure changes while fluid is flowing because i've read that it's wrong to think that change of velocity causes change of pressure but change of pressure which causes change of velcity.but the real cause of change of pressure is obstruction i cant also get exactly how this obstruction change pressure like when cross section decreases pressure decreases why?

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#### tiny-tim

Science Advisor
Homework Helper
Welcome to PF!

well,i ve some problems with bernouuli equation.first,i'd like to ask abt meaning of static pressure in flowing fluid because i really ve read abt that in references and many websites but still cant get exactly whats meaningt of static pressure in flowing fluid.
Hi ahmedbadr! Welcome to PF!

"static pressure" is the same as ordinary pressure (force/area).

(see http://en.wikipedia.org/wiki/Bernoulli's_principle#Simplified_form if you don't believe me! )

Some people say "static pressure" to distinguish it from "dynamic pressure" … but most people simply call it "pressure" … which is what it is! … I suggest you do the same!
i ve read on website that it's the pressure which exerted on plane parrallel to the flow while another website says static pressure in flowing fluid has direction normal to the flow.also before in reference that pressure ius scalal quantity (no direction) which means its equal on any point in all directions.
The third one is right … pressure is a scalar quantity (no direction) which means, at any point, it's equal in all directions.

I think these websites are choosing to measure the pressure on a particular plane, or in a particular direction, for a particular calculation … they're ignoring all the other planes or directions because they don't need them.
that was my 1st question ,my 2nd question abt what makes this static pressure changes while fluid is flowing because i've read that it's wrong to think that change of velocity causes change of pressure but change of pressure which causes change of velcity.but the real cause of change of pressure is obstruction
It's really the size of the pipe (or, as you say, the obstructions) which causes both the change in velocity and the change in pressure.

(though, of course, if you change the pressure at the beginning of the pipe, you will change the velocities all the way along the pipe)
i cant also get exactly how this obstruction change pressure like when cross section decreases pressure decreases why?
Because conservation of mass means that if the pipe is narrower, the fluid must go faster, and then conservation of energy (Bernoulli's equation) means that the pressure must go down!

#### russ_watters

Mentor
i ve read on website that it's the pressure which exerted on plane parrallel to the flow while another website says static pressure in flowing fluid has direction normal to the flow.
Those two statements are equivalent to each other.
also before in reference that pressure ius scalal quantity (no direction) which means its equal on any point in all directions.
The reason that static pressure is measured in a particular direction is that it is the pressure of the stationary fluid. But since the fluid isn't stationary, you'd need to have the pressure sensor moving with the fluid to measure the static pressure. Or, to avoid that, you measure the pressure in a direction where the velocity component of the fluid is zero: perpendicular to the direction of flow.
that was my 1st question ,my 2nd question abt what makes this static pressure changes while fluid is flowing because i've read that it's wrong to think that change of velocity causes change of pressure but change of pressure which causes change of velcity.but the real cause of change of pressure is obstruction i cant also get exactly how this obstruction change pressure like when cross section decreases pressure decreases why?
That seems like a chicken-or-egg question to me and I'm not sure it has a good answer.

#### minger

Science Advisor
that was my 1st question ,my 2nd question abt what makes this static pressure changes while fluid is flowing because i've read that it's wrong to think that change of velocity causes change of pressure but change of pressure which causes change of velcity.but the real cause of change of pressure is obstruction i cant also get exactly how this obstruction change pressure like when cross section decreases pressure decreases why?
That seems like a chicken-or-egg question to me and I'm not sure it has a good answer.
I agree. When calculating certain variables, it becomes an iterative process, kind of saying that one doesn't affect the other, they both happen simultaneous. An increase in pressure loss causes a decrease in velocity, which causes a decrease in Reynolds, which can cause a decrease in friction factor which can cause a decrease in the pressure loss, etc, etc.

#### ahmedbadr

well thx 4 ur reply but i already know what u explained but things still not clear for example when u say static pressure is force per area i already know that and can imagine his definition in static fluid but can imagine or feel this meaning in flowing fluid thats 1st 1st point .2nd point u say pressure changes when pipe size changes as change in pipe size acts an obstruction i also know that what i ask abt is on the molecular or microscopic scale why this obstruction makes pressure changes? and answer of this question i think shouldn be away from conservation of energy because as i say this presurre difference which makes velcity change and pressure changes due to existence of obstruction so question is how this obstruction changes static pressure?
what si the source of static pressure in flowing fluid? how does it vary when flow exposed 2 obstruction? these my questions because iam really confused abt static pressure in flowing fluid

#### russ_watters

Mentor
The "why" is Bernoulli's law: the total pressure along a streamline is constant. As tim said, that's a consequence of conservation of energy.

I'm not sure if that's what you are looking for, though - these questions seem circular to me.

Also, I'd appreciate it if you wouldn't type with text-speak. We try to maintain a level of seriousness in this forum.

#### ahmedbadr

first of all thx russ
2nd sorry what do u mean with text-speak?and whats relation between that and seriousness iam serious if iam not y i would type all these texts 2 get correct scientific information
3rd theses question are not circular they just need some one good at fluid mechanics and aware in good way of these concepts
again,what i say is pressure changes due 2 obstruction and this pressure difference causes fluid 2 accelerate (according to newton's second law f=ma)so causes fluid velocity 2 increase i cant get how this obstruction affects fluid pressure
i will try 2 explain y i 'd like 2 know , in piston cylinder system when gas is compressed its static pressure increases why? because as i think it's compressible fluid
so same number of molecules occupy smaller volume so rate of collisions between molecules and walls increases so static pressure increasesl

but lets compare that with a flowing liquid in pipe when cross section of pipe decreses
its pressure decreases??whay what happens to the fluid(liquid) particles so that static pressure decreases why pressure doesnt increase(as there's reduction in volume or rewduction in cross section) i hope i can make u get what i mean by my question

#### tiny-tim

Science Advisor
Homework Helper
Hi ahmedbadr!
Also, I'd appreciate it if you wouldn't type with text-speak. We try to maintain a level of seriousness in this forum.
I agree … your posts would be easier to understand if you wrote your words in full, and used less of them!
in piston cylinder system when gas is compressed its static pressure increases why?
Because it has nowhere to go!!

If the gas was flowing through a pipe whose cross-section decreased, its pressure would decrease … because it would have somewhere to go … and it would have to go faster, which means more kinetic energy, and that energy has to come from somewhere

(and unlike the piston, the pipe itself supplies no energy)

pressure is energy per volume (1 pascal = 1 joule per cubic metre) …

so more kinetic energy means less pressure.

#### ahmedbadr

ummm i think u still tell me same answer u think pressure decreases as velocity increases i dont know that exactly the reason or not but i think not u still answer me using conservation of energy law but i told u i want answer away from this law
i want answer in the microscopic scale i think i told the vreasons before
anyway thx all for all of ur replies

#### russ_watters

Mentor
I don't mean to be mean here, but I think the problem here is that The Answer just plain isn't in the form that you want. That isn't our fault, it's yours - you are asking something that isn't reasonable.

Ie: there is no separate microscopic explanation of Bernolli's Principle.

#### stewartcs

Science Advisor
ummm i think u still tell me same answer u think pressure decreases as velocity increases i dont know that exactly the reason or not but i think not u still answer me using conservation of energy law but i told u i want answer away from this law
i want answer in the microscopic scale i think i told the vreasons before
anyway thx all for all of ur replies
The molecules within a fluid are in constant random motion and collide with each other and with the walls of an object in the fluid. The motion of the molecules gives the molecules a linear momentum. The fluid pressure is a measure of this momentum. If a gas is at rest, all of the motion of the molecules is random and the pressure that one typically detects (e.g. with a pressure gauge) is the total pressure of the gas. If the gas is set in motion or flows, some of the random components of velocity are changed in favor of the directed motion. The directed motion is called ordered, as opposed to the disordered random motion.

Some of the total pressure is associated with the momentum of the ordered motion of the gas. This pressure is referred to as the dynamic pressure. The remaining random motion of the molecules still produces a pressure called the static pressure.

At the molecular level, there is no distinction between random and ordered motion. Each molecule has a velocity in some direction until it collides with another molecule and the velocity is changed. However, when one sums all of the velocities of all the molecules one will detect the ordered motion.

From the conservation of energy and momentum, the static pressure plus the dynamic pressure is equal to the original total pressure in a flow.

CS

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