TBR Physics chpt 7 P22

[FeinMS]

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Hey all, I need some help on this question.
The correct answer is C. I understand why there will be lowre fluid velocity at point B. But I don't understand why fluid height in column 1 will remain unchanged. Thanks!

 

[sazerac]

Bump. I am really curious as to the answer to this one.

My guy reaction is that a slower speed would result in more pressure, due to Bernoulli. So I want to know why I'm wrong.

 

[FeinMS]

Here's what TBR says about that part of the answer, "... The fluid heights in the columns depends upon the pressure below each column in the drainage tube. The pressure difference across the drainage tube depends upon the pressure at the reservoir end (which is due to the weight of the fluid) and the pressure at the exit end (which is due to the atmosphere). Since neither pressure changes, the introduction of the new fluid (whose mass density is equal to that of the previous fluid) will not affect the fluid heights in the column.

I have no idea what this is saying.

 

[sazerac]

It is saying that after you swap one fluid for another, the pressure at point A will not change, because that pressure depends on the density of the fluid and the densities are the same.

It is saying that the pressure at B remains the same, because it is exposed to the atmosphere.

So it concludes that the pressure difference between A and B will be the same along the whole pipe, so the height will be the same.

I am just not sure why Bernoulli doesn't apply here.

 

[sshah92]

Hey all, I need some help on this question.
The correct answer is C. I understand why there will be lowre fluid velocity at point B. But I don't understand why fluid height in column 1 will remain unchanged. Thanks!

Well viscosity is resistance to flow, so if viscosity increases then the fluid velocity will decrease at point B. As for why fluid height doesn't change, let's first look at the factors that impact height of a fluid in a column.

Pressure = density,fluid * gravity * height + P,atmosphere

Does P,atmosphere change? No.
Does pressure change at any place, in fact? No.
Does density change? The problem actually says it doesn't.

So when you solve for height, you'll see that all the variables are the same here -- and therefore the answer is C! Hope that helps.

 

[FeinMS]

It is saying that after you swap one fluid for another, the pressure at point A will not change, because that pressure depends on the density of the fluid and the densities are the same.

It is saying that the pressure at B remains the same, because it is exposed to the atmosphere.

So it concludes that the pressure difference between A and B will be the same along the whole pipe, so the height will be the same.

I am just not sure why Bernoulli doesn't apply here.

Probably because of high viscosity? High viscosity is a deviation from being ideal and Bernoulli applies to ideal fluid.

Well viscosity is resistance to flow, so if viscosity increases then the fluid velocity will decrease at point B. As for why fluid height doesn't change, let's first look at the factors that impact height of a fluid in a column.

Pressure = density,fluid * gravity * height + P,atmosphere

Does P,atmosphere change? No.
Does pressure change at any place, in fact? No.
Does density change? The problem actually says it doesn't.

So when you solve for height, you'll see that all the variables are the same here -- and therefore the answer is C! Hope that helps.

Thanks a lot. So let's say I want to find the height of column. So I solve for h.
h= (Pressure-P,atmosphere)/(density,fluid*gravity) What would be "Pressure" referring to? Is it just Pressure at point A? which will be density,fluid*gravity*(height of A)?

 

[sshah92]

It is saying that after you swap one fluid for another, the pressure at point A will not change, because that pressure depends on the density of the fluid and the densities are the same.

It is saying that the pressure at B remains the same, because it is exposed to the atmosphere.

So it concludes that the pressure difference between A and B will be the same along the whole pipe, so the height will be the same.

I am just not sure why Bernoulli doesn't apply here.

Bernoulli's Principle does apply here! Bernoulli's principle states that overall energy is conserved during flow, at any time point. Note that this principle is only intended to compare initial and final stages of flow for a liquid in a single system. And here you see that both types of liquids are observed independently of each other, so using the principle won't help.

Alright, so I wanted to make sure you understand that before I delve into this further. Because in this question, although I said that Bernoulli's Principle isn't supposed to be used (since it's two different systems), you actually CAN use the formula. But only because both liquids have the same density, start out at the same height, and start out with the same pre-flow velocity (of 0 m/s). Once you see that all of these variables are the same, you'll realize that height won't differ from one system to another, and that will simply reinforce the answer choice of C.

Of course, you're not supposed to put thaaat much thought into it. They really just want you to realize that height is directly proportional to the change in pressure. If that doesn't change, height won't either.

 

[sshah92]

Probably because of high viscosity? High viscosity is a deviation from being ideal and Bernoulli applies to ideal fluid.



Thanks a lot. So let's say I want to find the height of column. So I solve for h.
h= (Pressure-P,atmosphere)/(density,fluid*gravity) What would be "Pressure" referring to? Is it just Pressure at point A? which will be density,fluid*gravity*(height of A)?

Yup. It's the pressure at the very bottom of the apparatus. So that's point A.