Pressure (Bernoulli's equation)

[Hemichordate]

So according to Bernoulli's equation, when you increase the area, increase the pressure.

BUt when you look at the formula P = F/A, when you increase the area, the pressure decreases.

Is there a reason for this paradox?

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[loveoforganic]

Nvm, definitely wasn't right in what I was saying.

 

[wanderer]

So according to Bernoulli's equation, when you increase the area, increase the pressure.

BUt when you look at the formula P = F/A, when you increase the area, the pressure decreases.

Is there a reason for this paradox?

Think about when you apply Bernoulli's equation and when you use P=F/A.

 

[Hemichordate]

Think about when you apply Bernoulli's equation and when you use P=F/A.

I know Bernoulli is used when you have something like a circular tube with fluid flowing through and the other is pressure on a surface. Is that the only difference?

 

[nanaschool2000]

So according to Bernoulli's equation, when you increase the area, increase the pressure.

BUt when you look at the formula P = F/A, when you increase the area, the pressure decreases.

Is there a reason for this paradox?

Think about doing car wash by using a hose (w/o pressure gun). If you squeeze the end of hose and decrease the area, water will come out fasterw/ more pressure.

Same reason why blockage in artery due to the fat droplets cause high blood pressure.

 

[Hemichordate]

Think about doing car wash by using a hose (w/o pressure gun). If you squeeze the end of hose and decrease the area, water will come out fasterw/ more pressure.

Same reason why blockage in artery due to the fat droplets cause high blood pressure.

Huh? I thought when you decreased the area of a pipe, the velocity of fluid flowing through increased and the pressure decreased.

 

[nanaschool2000]

YOu are right. I was confused. What I was going to say was the pressure goes from high pressure to low pressure when the area converts from large to small. Thanks for correcting me.

 

[SuperSaiyan3]

Huh? I thought when you decreased the area of a pipe, the velocity of fluid flowing through increased and the pressure decreased.

?!

Even I know that when you increase the area of a pipe, the velocity of fluid flowing through DECREASES.

Think streamlines. When fluid flows from a smaller area pipe to a larger one, the streamlines get more spread apart. THIS is Bernoulli's concept. Or somebody else's. I don't care.

But the point is, the more streamlines are spread out, the slower the velocity. The more cramped streamlines are, the faster they are gonna be going.

- SS3

 

[wanderer]

So according to Bernoulli's equation, when you increase the area, increase the pressure.

BUt when you look at the formula P = F/A, when you increase the area, the pressure decreases.

Is there a reason for this paradox?

The problem is that in fluid dynamics, if you change the area F is not kept constant.
Bernoulli's equation is used together with the continuity equation (Q=A*v=constant), so if you have a closed system raising A lowers v which raises pressure. Clearly F is also raised due to the lower velocity.

 

[minutemen11]

The problem is that in fluid dynamics, if you change the area F is not kept constant.
Bernoulli's equation is used together with the continuity equation (Q=A*v=constant), so if you have a closed system raising A lowers v which raises pressure. Clearly F is also raised due to the lower velocity.

i do not get this at all...
if you have a garden hose and then cover a portion of the hose opening with your finger, both pressure because P=F/A and velocity (Av=Av) increases.. this seems like it is violating Bernoulli's principle.. i know that principle states that pressure increases while velocity decreases only when the two points are at the same height... i think im confused because when water leaves the hose it disperses everywhere and is not restricted to the area of the hose anymore.. so if this hose were connected to a smaller diameter hose the velocity would increase but i have a hard time visualizing how the heck pressure would drop..
help

 

[minutemen11]

bumpp
who gets this???

 

[stockraider]

ok, here from what i understand your question is why is velocity high when pressure is low. you should understand that HIGH fluid velocity CAUSES there to be lower pressure, basically pressure is lower where the flow velocity is greater, meaning that pressure in this case is dependent on the speed of fluid flow...all of you guys have been thinking that velocity is higher where pressure is lower, which is absolutely not the case....you can't just turn the statement in bold around..bernoulli says pressure is a function of velocity of the fluid, not vice versa.

think about it this way, pressure is charectarized as fluid hitting the walls of the tube, if the fluid is moving fast, most of the molecules are going to have forward movement through the lumen of the tube and are not going to have the "time and energy" to hit the walls of the tube.

to think of it emperically note the bernoulli equation:
P1+ 1/2(rho)v1^2+(rho)g*h1=P2+1/2(rho)v2^2+(rho)g*h2.

at the same height the rho*g*h's cancel and you are left with

P1+1/2(rho)v1^2=P2+1/2(rho)v2^2

say you keep the left side of the equation constant then say you decrease the area of the hose for the right side of the equation, this means (via AV=AV) you have to increase velocity, if you increase v on the RIGHT side of the equation, then what is the ONLY variable on the right side that you can DECREASE to keep that total value the same? it is P2.

do NOT use P= F/A here to look at how pressure changes, it simply does not apply. F/A measures pressure due to acceleration, mass and the cross sectional area, NOT due to velocity of the fluid at the same heights. use benoullis when it comes to fluid flow.

 

[minutemen11]

ok, here from what i understand your question is why is velocity high when pressure is low. you should understand that HIGH fluid velocity CAUSES there to be lower pressure, basically pressure is lower where the flow velocity is greater, meaning that pressure in this case is dependent on the speed of fluid flow...all of you guys have been thinking that velocity is higher where pressure is lower, which is absolutely not the case....you can't just turn the statement in bold around..bernoulli says pressure is a function of velocity of the fluid, not vice versa.

think about it this way, pressure is charectarized as fluid hitting the walls of the tube, if the fluid is moving fast, most of the molecules are going to have forward movement through the lumen of the tube and are not going to have the "time and energy" to hit the walls of the tube.

to think of it emperically note the bernoulli equation:
P1+ 1/2(rho)v1^2+(rho)g*h1=P2+1/2(rho)v2^2+(rho)g*h2.

at the same height the rho*g*h's cancel and you are left with

P1+1/2(rho)v1^2=P2+1/2(rho)v2^2

say you keep the left side of the equation constant then say you decrease the area of the hose for the right side of the equation, this means (via AV=AV) you have to increase velocity, if you increase v on the RIGHT side of the equation, then what is the ONLY variable on the right side that you can DECREASE to keep that total value the same? it is P2.

do NOT use P= F/A here to look at how pressure changes, it simply does not apply. F/A measures pressure due to acceleration, mass and the cross sectional area, NOT due to velocity of the fluid at the same heights. use benoullis when it comes to fluid flow.

how would you solve a problem asking for the pressure of in a tube then? Lets say you're given Vintial and Vfinal but your not given the pressure of either tube. If water is flowing from a larger tube (area 10 lets say) with force 100N to a smaller tube (area 5) with an unknown force there is no way you can solve that problem without using P=F/A. This is exactly why I cant understand this intuitively. I am also assuming that the two pipes are at the same height level

helppp

 

[ese]

how would you solve a problem asking for the pressure of in a tube then? Lets say you're given Vintial and Vfinal but your not given the pressure of either tube. If water is flowing from a larger tube (area 10 lets say) with force 100N to a smaller tube (area 5) with an unknown force there is no way you can solve that problem without using P=F/A. This is exactly why I cant understand this intuitively. I am also assuming that the two pipes are at the same height level

helppp

You would use the flow rate equation (FR=Av) and P=F/A, not Bernoulli's equation.

 

[stockraider]

oh if they are asking for forces, then by all means, use p=f/a, otherwise make sure to use the bernoullis equation when they are talking about velocity.

 

[Tupaki0]

so you cant you apply these concepts to blood?

because vasodilatation (increasing area) decreases blood pressure and vasoconstriction (decreasing area) increases blood pressure

 

[stockraider]

vasoconstriction and vasodilation do not effect blood velocity directly, they simply are mechanisms to alter the pressure. it's all relative increased area causes decreased blood pressure against the walls of the vessel, this tells you nothing about the velocity of the blood and the equation P=F/A applies. remember when a blood vessel contracts, the entire thing contracts so there aren't two different areas where the area of one part of the vessel is greater than the area of another, if there was, then bernoulli would apply. remember that velocity determines pressure, but pressure does not directly determine velocity

 

[minutemen11]

"how would you solve a problem asking for the pressure of in a tube then? Lets say you're given Vintial and Vfinal but your not given the pressure of either tube. If water is flowing from a larger tube (area 10 lets say) with force 100N to a smaller tube (area 5) with an unknown force there is no way you can solve that problem without using P=F/A. This is exactly why I cant understand this intuitively. I am also assuming that the two pipes are at the same height level"

Ok so judging from all your responses, isnt this saying that velocity increases (Vfinal will obviously be greater than Vintial) AND the pressure increases from bernouli?

Im sorry i feel like im beating a dead horse but something isnt clicking. I understand your responses stockraider and ese but im have a hard time putting this into real examples.

 

[Cap'n]

I know I am late to the party, but I hope that some of you might be able to still confirm this as true. My impression is that P = F/A is to be used only for stagnant systems and Bernoulli's equation is to be used for systems with flow. That is, 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. However, if dealing with a stagnant system (say, some fluid in a container), then the fluid has all the time in the world to exert pressure on the walls because it isn't moving anywhere. Therefore, the larger the container, the less pressure on the walls, because the fluid has more space to spread out. The smaller the container, the more pressure on the walls.

 

[orangetea]

I know I am late to the party, but I hope that some of you might be able to still confirm this as true. My impression is that P = F/A is to be used only for stagnant systems and Bernoulli's equation is to be used for systems with flow. That is, 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. However, if dealing with a stagnant system (say, some fluid in a container), then the fluid has all the time in the world to exert pressure on the walls because it isn't moving anywhere. Therefore, the larger the container, the less pressure on the walls, because the fluid has more space to spread out. The smaller the container, the more pressure on the walls.

That's the way I have learned it.. for problems involving change of height, velocity, or pressure I just use B's equation and see which two terms (P, PHG, 1/2pv2) is constant and which one is changing. P=F/A is applied to stagnant systems, I don't think it's appropriate to apply it to flow equations because like others have mentioned two terms are changing while only one is constant so it wouldn't really yield any information. But correct me if I am wrong