TBR question 15, Fluids and Solids

[Pamplemousse123]

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TBR question #15, pg 78: fluids and solids -


The question is :
what will be observed when a more viscous liquid of same mass denisty is substituted for the less viscous liquid in the experiment?
C. A lower fluid velocity at point D, but an unchanged fluid height in Columns 1 2 and 3
D. A lower fluid velocity at point D and greater fluid height in Columns 1,2,3

I chose D (answer is C) because if you have a lower fluid velocity, not as much fluid is going out D per second and thus you have more fluid inside the apparatus - shouldn't the columns then be higher than what figure 2 presents?

The answer key says that the height of the columns are determined by pressure and since pressure is constant, height is constant (C is the answer) - is this relationship from the bernouilli equation? If it is, shouldn't velocity also affect the height and a lower velocity, constant pressure means a higher height?

The same arugment goes with question 17-
if the end of the drain pipe were pinched in such a way that the internal diameter at D is reduced, how will the height be affected: If drain pipe decreases its area - it increases the velocity according to the continuity equation, so more fluid will be pushed out and heights should decrease - and accroding to bernouilli - if pressure is constant, velocity is increased then height should decrease. The answer to this problem is that the heights will be the same.

Another one with the same concept being tested - 18: if the columns' radii were decreased and flow rate is the same, shouldn't the height of the liquid increase. it seems very counterintuitive that the heights will be the same because the flow rate is same - i feel like there is a "conservation of fluid" being violated.

Maybe I'm misinterpreting the questions. Can somebody please clarify? Thanks in advance!

 

[BerkReviewTeach]

TBR question #15, pg 78: fluids and solids -


The question is :
what will be observed when a more viscous liquid of same mass denisty is substituted for the less viscous liquid in the experiment?
C. A lower fluid velocity at point D, but an unchanged fluid height in Columns 1 2 and 3
D. A lower fluid velocity at point D and greater fluid height in Columns 1,2,3

I chose D (answer is C) because if you have a lower fluid velocity, not as much fluid is going out D per second and thus you have more fluid inside the apparatus - shouldn't the columns then be higher than what figure 2 presents?

The answer key says that the height of the columns are determined by pressure and since pressure is constant, height is constant (C is the answer) - is this relationship from the bernouilli equation? If it is, shouldn't velocity also affect the height and a lower velocity, constant pressure means a higher height?

The same arugment goes with question 17-
if the end of the drain pipe were pinched in such a way that the internal diameter at D is reduced, how will the height be affected: If drain pipe decreases its area - it increases the velocity according to the continuity equation, so more fluid will be pushed out and heights should decrease - and accroding to bernouilli - if pressure is constant, velocity is increased then height should decrease. The answer to this problem is that the heights will be the same.

Another one with the same concept being tested - 18: if the columns' radii were decreased and flow rate is the same, shouldn't the height of the liquid increase. it seems very counterintuitive that the heights will be the same because the flow rate is same - i feel like there is a "conservation of fluid" being violated.

Maybe I'm misinterpreting the questions. Can somebody please clarify? Thanks in advance!

This isn't exactly Bernoulli's principle. It has to do with flow dynamics. If you consider a pipe of flowing fluid, it must have higher pressure at one end than the other (deltaP is necessary to generate the flow). At the midway point in a pipe with a uniform flowing fluid, the pressure should be an average of the two end pressures. This is to say that the pressure drops off uniformly as it flows from a region of higher pressure to a region of lower pressure. No matter what ideal liquid they are using, the pressure drop from one end to the other should be the same. What this question assumed was constant pressure difference between the two ends of the pipe, which is reasonable as long as the weight of the fluid in the reservoir didn't change (which is probably why they said the density remains the same).

The result is that the pressure pushing up any given side tube should be the same with either fluid.

Does that make sense?

 

[Pamplemousse123]

Thanks for the explanation. I can semi see why the height is unchanged - the only problem is if there is lower flow velocity or rate at D than what the figure represents , where is the additional fluid that did not come out of the apparatus? Shouldn't it be back in the columns which will then increase the height of the columns as compared to the figure?

 

[IntelInside]

One of the problems with your logic is this:

Bernoulli's equation ONLY deals with ideal fluids. Since this fluid has viscosity it can not be considered to follow bernoulli's equation.

But one of the problem's I am having in seeing this is that even though this is not an ideal fluid, it's viscosity it taking away some of uniform kinetic energy therefore it should have a greater random ke which does contribute to pressure.

 

[Pamplemousse123]

Does anyone see a problem of not conserving fluid with the heights being unchanged? Enlighten me!

 

[Pamplemousse123]

BUMP!

I'm just dying to know where the fluid goes!

If the velocity is lowered at point D, that means there is some fluid that didn't go out as compared to figure 2 - this means that extra fluid remained somewhere in the apparatus, so the heights must increase in comparison to the figure!

 

[BerkReviewTeach]

BUMP!

I'm just dying to know where the fluid goes!

If the velocity is lowered at point D, that means there is some fluid that didn't go out as compared to figure 2 - this means that extra fluid remained somewhere in the apparatus, so the heights must increase in comparison to the figure!

It definitely flows out slower in the new scenario. But the question is not asking about flow speed, but rather, the height in columns along the path. This is a question of pressure drop as a fluid flows through a pipe.

Think about it this way. If you closed the valve, then the pressure at each end of the tube would have to balance, because flow will stop and Pascal's Principle says the fluid must distribute its pressure evenly. When you open the valve again, the fluid will begin to flow (because of the pressure difference), so the fluid in the right side of the pipe must be a lower pressure than the left side of the pipe. Any points along the pipe that have a hole and vertical tube will have fluid climb them according to the pressure of the fluid at that point. Notice that each pipe has a gradually decreasing height from left to right, as would be expected with a decreasing pressure gradient from left to right.

The difference in speed is not the reason for the height difference, as the speed should be the same at all points along the pipe. The height difference is because of natural pressure drop associated with a flowing fluid. The change in viscosity is there to throw people of the scent and make them think about Bernoulli's principle when they shouldn't. This is a Pousielle's question!

 

[IntelInside]

It definitely flows out slower in the new scenario. But the question is not asking about flow speed, but rather, the height in columns along the path. This is a question of pressure drop as a fluid flows through a pipe.

Think about it this way. If you closed the valve, then the pressure at each end of the tube would have to balance, because flow will stop and Pascal's Principle says the fluid must distribute its pressure evenly. When you open the valve again, the fluid will begin to flow (because of the pressure difference), so the fluid in the right side of the pipe must be a lower pressure than the left side of the pipe. Any points along the pipe that have a hole and vertical tube will have fluid climb them according to the pressure of the fluid at that point. Notice that each pipe has a gradually decreasing height from left to right, as would be expected with a decreasing pressure gradient from left to right.

The difference in speed is not the reason for the height difference, as the speed should be the same at all points along the pipe. The height difference is because of natural pressure drop associated with a flowing fluid. The change in viscosity is there to throw people of the scent and make them think about Bernoulli's principle when they shouldn't. This is a Pousielle's question!

I understand that there should be a pressure difference from one end to the next and I just want to make sure I have this correct

We see that volumetric flow rate and viscosity have a 1:1 inverse relationship and since pressure is proportional to mass only in this case because it is a real fluid and the relationship between velocity and pressure, derived from bernoulli's, doesnt apply here. Correct?

 

[Pamplemousse123]

TBRteach,
sorry to pester you about these questions, but your explanations are extremely helpful.

Please confirm that if the fluid in this case were ideal, then the heights of the columns would decrease because of the bernouilli eqn.

If you know of any, can you also tell me about a home experiment that I can perform to see that the heights don't increase? I am having a problem visualizing that the heights remain the same. Otherwise , it makes sense with the equations.

thanks!