Fluid Dynamics questions

[September24]

1.As far as fluids go, what conditions can cause fluid flow (Q) to change. Fluid flow usually remains constant since if A increases, V decreases and vice versa but when do I consider that it is NOT CONSTANT.

2.Can someone basically explain the concepts behind hot air balloon problems. I always get so flustered when seeing these passages. I understand that Bernoulli’s is the main concept but how should I always approach these problems. Are there any tips anyone can give or recommend good websites.

3.In section 7 (Fluids and solids) of Berkeley review, it deals with buoyant force of submerged balls. It provides two questions. In the first one, when three balls of same density but different volumes are submerged, it asks which has same acceleration when all balls are let go. Since densities are same, they each experience the same acceleration upwards. This means that buoyant force is independent of volume here. However, in the next problem, it states that when a ball is compressed, it looses volume which decreases buoyant force due to less volume being displaced. So which is it? Is buoyant force independent or dependent on volume?

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[Gauss44]

3.In section 7 (Fluids and solids) of Berkeley review, it deals with buoyant force of submerged balls. It provides two questions. In the first one, when three balls of same density but different volumes are submerged, it asks which has same acceleration when all balls are let go. Since densities are same, they each experience the same acceleration upwards. This means that buoyant force is independent of volume here. However, in the next problem, it states that when a ball is compressed, it looses volume which decreases buoyant force due to less volume being displaced. So which is it? Is buoyant force independent or dependent on volume?

The buoyant force is dependent on the volume of fluid displaced. Regarding the balloons, if the densities are the same, then the masses will vary if the volume varies. That will impact the force up (mg of fluid displaced) versus force down (mg of contents in balloons and maybe the balloons themselves).

 

[September24]

Hmmmm...I'm still a bit confused. Why did volume matter in one question but not in the other?

 

[krogers21]

The buoyant force is dependent on the volume of fluid displaced. Regarding the balloons, if the densities are the same, then the masses will vary if the volume varies. That will impact the force up (mg of fluid displaced) versus force down (mg of contents in balloons and maybe the balloons themselves).

OP, I believe that what Gauss is saying is that in question 3, it states "three balls of same density but different volumes" so therefore since density can be in terms of mass/volume, equal density with different volumes means equivocally different masses in order to create equal densities.

Think of a balloon - filling the balloon with air and placing it on a body of water, the balloon will float because the balloon has a certain volume wherein the buoyancy force equals the weight of the balloon. However, if you fill the balloon with sand (or rocks, or anything else more dense), then the balloon will sink. Why is this? This is because the volume of the balloon stays the same, but the weight of the balloon is larger than the buoyancy force, so it will sink.

So in the grand scheme of things, the different mass means different weight. The different volume means different buoyancy force. Density is a ratio of mass and volume, so the equal density means the weight-to-buoyancy force ratio is equal in all of the. BUT, this does not mean the weight nor the volume are the same - in fact, none of them are. To answer your question, volume matters in both questions.

As a disclaimer, I've not really studied buoyancy yet so I may be wrong but I think this is correct. The basis of my statement came from this website(which I think explains the concept perfectly): http://popphysics.com/chapter-4-fluid-mechanics/buoyancy/