Question

I am confused.. Pressure = force/area and by bernoulli's theorem "pressure is directly proportional to area " but this is contradicting the first formula...

Answer 1

@ganeshie8 @pooja195 @whpalmer4

Answer 2

am i missing a point.. ? if so what is it?

Answer 3

@ganeshie8 asked a very similar question once :)

Answer 4

Also, area of the cross-section is not the same as the area of the walls. I guess that's one point to note but I'm still thinking of a proper reason.

Answer 5

yeah even i considered that point but later thought that kind of reasoning was pretty vague..so could u explain a bit more?

Answer 6

@Beauregard @Michele_Laino

Answer 7

@satellite73 can u help

Answer 8

@zepdrix @dan815

Answer 9

@inkyvoyd

Answer 10

@Kkutie7 @agent0smith can u help?

Answer 11

no I'm sorry =(

Answer 12

its ok..thanks for trying!

Answer 13

@Beauregard did u get a proper reason??

Answer 14

I would think that the area mentioned in Bernoulli's theorem is referring to the area of the fluid? And pressure is using area meaning the area of the container

Answer 15

Bernoulli's formula gives the pressure within the fluid, not necessarily exerted on the walls.

Answer 16

Yeah that's essentially what I meant. Worded better though

Answer 17

@agent0smith can u explain a bit more

Answer 18

@nuttyliaczar can u explain?

Answer 19

@agent0smith r u there?

Answer 20

Maybe this will help: http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html#beq

and the part about pressure as energy density http://hyperphysics.phy-astr.gsu.edu/hbase/press.html#ed

Answer 21

Keep in mind that Bernoulli's equation relates to pressure in a moving fluid.

"In the high velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy."

Answer 22

oh so pressure=force / area --fluid statics
bernoulli's eq --fluid dynamics
but still when we relate both to area..they contradict why?

Answer 23

i saw your link too..they explain bernoulli's eq and pressure..but i want to know why the relation with area is the opp just because the fluid is moving

Answer 24

?

Answer 25

are u there?

Answer 26

??

Answer 27

Be patient.

They don't really contradict. Static pressure is due to molecules bouncing off the sides of a container.

The pressure term in bernoulli's equation gives the pressure within the fluid, but keep in mind you can't just ignore the kinetic energy term. The reason the pressure decreases when area decreases, goes back to the flow rate (volume/time) which remains constant throughout a fluid. The flow rate remains constant because of conservation of mass (remember the water has inertia)

When the area decreases, the velocity must increase for flow rate to remain constant. If velocity increases, the kinetic energy therefore increases... which means the pressure has to decrease (because the total energy of the fluid is conserved).

If you put a large wooden board into a stream of fast moving water, you'll feel a lot of pressure on the board - due to the high kinetic energy of the water, as well as the pressure of the water molecules randomly bouncing off the wall (which you'd similarly feel if the water was stationary).

Answer 28

There's also the fact that "a fluid that is flowing through a pipe with a high velocity doesn't "have time" to exert pressure on the walls, but one with a lower velocity does, which means that pressure is higher when velocity is lower, and velocity is lower when cross-sectional area of the pipe is larger"

http://forums.studentdoctor.net/threads/pressure-bernoullis-equation.649415/

Answer 29

ok..sry for not being patient..what will be the pressure of a liquid (stationary) inside a pipe..? it exerts pressure on the walls of the pipe ..so to find that pressure will i do mg of the liquid per unit surface area of the pipe? here the area of cross section of the pipe is immaterial right? we will need it only when water is "flowing"..right? is that the point that i missed? is my understanding correct?

Answer 30

In the case of stationary fluid, the pressure depends on depth. Remember that the pressure isn't the same at all points in a pipe, it'll be higher at the base (more weight of water above) and will decrease from there on up.

Yes I think that's right. Cross sectional area of the fluid isn't the same as the area of the walls.

Answer 31

Another reason why the flow rate of a fluid remains constant, because of conservation of mass, is that the mass per unit time must remain constant. Just adding to what I said about the water having inertia.

Just like a solid object will continue moving at constant velocity due to inertia, the total mass of a fluid must also move at constant velocity.

So if cross sectional area of the fluid decreases, the velocity must increase, for the mass per unit time to remain constant. Smaller cross sectional area means a smaller mass of water can "fit" in the smaller area. This assumes constant density and the fluid is incompressible.

If the velocity didn't increase, there would be less mass of water moving past a point in a given time, meaning the velocity of the total mass of water must have decreased.

Answer 32

yeah! i learnt these under the topic continuity eq..

Answer 33

ok..so may i conclude that both "area"s are diff and one eq is talking abt the fluid at rest and the other when its in motion..so both eqs are for diff situations..so we can't really generalise the relation between P and A..right?

Answer 34

@agent0smith

Answer 35

Yes, one is cross sectional area of the fluid, the other is area that the fluid is in contact with the walls of its container.

And yes, both equations are for different situations.

Answer 36

thanks a lot!

Answer 37

You're welcome.

Answer 38

would u mind helping me in another Q..?

Answer 39

Eh, maybe, depends how long it is. I'll take a look.

Answer 40

its a problem on fluid dynamics

Answer 41

wait i'll post it..