TPRH Science Workbook Passage 15 #1

[aspiringdoc09]

I attached a drawing to represent the figure given.

#1 Which of the following correctly relates the pressure readings obtained from each pressure gauge in terms of the locations at which the gauges are situated?

Note: I typed incorrectly in place of correctly. It is correct now.

A. P1 < P2 < P3
B. P1<P2 = P3
C. P1 = P2 < P3
D. P1 > P2 > P3

Why would the pressure be less where there is more velocity? Also, I thought that P=F/A, so wouldn't it be inversely proportional to the area too, and that would make it higher in section 3. I cannot understand the justification that based on Bernoulli's effect an increase in velocity correlates to lower fluid pressure.

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[syoung]

the question asks for INCORRECTLY... so does that mean P1>P2>P3 is the wrong relationship of the pressure readings?
and Bournelli:
1/2 v^2 + gh + P/(rho) = constant , where rho = density
And as the cross sectional area gets smaller, the v goes up in that particular areas, so:
as you pass to a smaller area, the v goes up. as v goes up, there is no change in Height or density, and since this is one fluid, the constant is constant. Therefore the only thing that can change as v goes up is for P to go down.

 

[aspiringdoc09]

the question asks for INCORRECTLY... so does that mean P1>P2>P3 is the wrong relationship of the pressure readings?
and Bournelli:
1/2 v^2 + gh + P/(rho) = constant , where rho = density
And as the cross sectional area gets smaller, the v goes up in that particular areas, so:
as you pass to a smaller area, the v goes up. as v goes up, there is no change in Height or density, and since this is one fluid, the constant is constant. Therefore the only thing that can change as v goes up is for P to go down.

I meant correctly. I will edit it and put it in bold. sorry.

 

[syoung]

http://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html

This says same thing, decreasing area = increasing velocity and increasing velocity = decreasing pressure for a given height

 

[chiddler]

i'm very happy you made that edit

 

[aspiringdoc09]

I just don't understand why an increase in velocity doesn't correlate to an increase in pressure. Is it because the fluid moves so fast that pressure cannot be applied? I don't understand this concept; the Bernoulli effect. I can't bridge it together in my mind. Sure, I can accept it as true, but WHY IS IT TRUE?

 

[chiddler]

I just don't understand why an increase in velocity doesn't correlate to an increase in pressure. Is it because the fluid moves so fast that pressure cannot be applied? I don't understand this concept; the Bernoulli effect. I can't bridge it together in my mind. Sure, I can accept it as true, but WHY IS IT TRUE?

Think of pressure in molecular terms. What does it mean? It's when particles are pushing against some surface of an object.

What if those particles all start moving in the same direction? Now they aren't hitting that object anymore because they have some directed movement. Therefore, as velocity increases, pressure decreases because they are hitting surfaces less than if they were not.

here

 

[aspiringdoc09]

Think of pressure in molecular terms. What does it mean? It's when particles are pushing against some surface of an object.

What if those particles all start moving in the same direction? Now they aren't hitting that object anymore because they have some directed movement. Therefore, as velocity increases, pressure decreases because they are hitting surfaces less than if they were not.

here

Ok. I can see that now when we put it into molecular terms. But why wouldn't an increase in the area decrease pressure (P=F/A)? Or does this relationship not apply here? Because if I think in terms of P=F/A and Q=Av; then, increasing area decreases velocity and pressure.

 

[chiddler]

Ok. I can see that now when we put it into molecular terms. But why wouldn't an increase in the area decrease pressure (P=F/A)? Or does this relationship not apply here? Because if I think in terms of P=F/A and Q=Av; then, increasing area decreases velocity and pressure.

edit: i'm not certain, but I think this is why.

too many variables.

like asking if ab=cd, and I change c and d, how does anything else change? we can't figure that out unless we have more info.

similarly, you have P = FV/Q. The only constant is Q. Everything else is variable.

Hmm..is F indeed a variable or is it constant? Either way, too many variables. But i'd like to know about F if anybody cares to comment.

 

[aspiringdoc09]

too many variables.

like asking if ab=cd, and I change c and d, how does anything else change? we can't figure that out unless we have more info.

similarly, you have P = FV/Q. The only constant is Q. Everything else is variable.

Hmm..is F indeed a variable or is it constant?

Thank you Chiddler! I tend to overanalyze everything, and I think that is a trap for me.

 

[chiddler]

Thank you Chiddler! I tend to overanalyze everything, and I think that is a trap for me.

sorry about constant editing. was a thinking process for me, too

 

[Buttafuoco]

Haha, silly TS thinking there's a way to think that the Bernoulli effect can be made intuitive!

But like Chidder was saying, pressure in these types of systems is due to the random movement of a fluid. With a liquid, we're not compressing it when it goes to a smaller pipe. They're incompressible for our purposes. What we're doing is making the same volume of liquid go through an area faster, and so in any given area there are going to be fewer molecules randomly running into a given area of pipe.