2 Fluid Force Questions: What's the Difference and Why?

[justadream]

TPR SW #210

“A circular plate with area of 1m^2 covers a drain hole at the bottom of a tank of water which is 1 m deep. Approximately how much force is required to lift the cover if it weighs 2000N?

TPR Answer: F = PA = rho*g*d*A = 1000 * 10 * 1 * 1 = 10000N . Since the drain hole weighs 2000N, total force needed = 10000 + 2000 = 12000

Why is the weight of the cover (2000N) taken as is? Shouldn’t it be decreased because there is a buoyant force (by virtue of the drain hole cover being submerged in the fluid) that should make the apparent weight < actual weight?


In addition, why is the set-up for this question different from that below (in other words, why does the question above use gauge pressure while the question below use buoyant force and simple "mg")?

TPR SW #243

“A hollow .2kg ball is released from the bottom of a pool and is propelled upward by a 9N buoyant force. The depth of the pool is 2m. If frictional forces were neglected, with what speed would the ball reach the surface (use g = 10)


TPR’s answer uses: Fnet = Buoyant_Force – weight

= Buoyant_Force – mg

EDIT: Also with regard to the 2nd question, why don't you account for gauge pressure in it? Doesn't the object feel some pressure from being under the water?

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[Cawolf]

I take the first question as the drain hole cover being completely under water, with no water under it pushing up - so there would be no buoyant force. Also without a volume we have no way of solving for it. So I would take it as the plate being contiguous with the floor.

 

[justadream]

@Cawolf
Thanks for your response as always.

But what about in the process of lifting it up? The instantaneous moment you lift it above water by like .00001m, wouldn't there by a buoyant force?

Also, why isn't gauge pressure included in "apparent weight" calculations regarding fluids?

 

[Cawolf]

Yes I think that once you lifted it it would experience a buoyant force, but also water would start draining and it would change the whole problem. I have found that the simplest situation usually is the best to look at first.

Even if we wanted to include the buoyant force we couldn't, because we don't know the volume displaced.

Did it specify if the tank was open to the atmosphere? I couldn't answer that exactly so I was reading a text and it seems like it is not used unless the object is being taken out of the water. Sorry I don't have a better answer!

 

[el_duderino]

They're looking for the force to break the seal, as it were. It's a drain plug. If you apply 11000 N to the plate, nothing happens. It doesn't move. Doesn't matter if 11000 N will let you lift it after the drain is opened.

 

[justadream]

@jonnythan

Thanks! That makes sense.

With regard to my second question:
TPR SW #243

“A hollow .2kg ball is released from the bottom of a pool and is propelled upward by a 9N buoyant force. The depth of the pool is 2m. If frictional forces were neglected, with what speed would the ball reach the surface (use g = 10)


TPR’s answer uses: Fnet = Buoyant_Force – weight

= Buoyant_Force – mg

How come you don't include gauge pressure in the calculation?

 

[el_duderino]

Why would pressure come into play at all in this scenario? Pressure won't affect force due to gravity or the buoyant force (which is essentially the mass of water displaced).

 

[justadream]

@jonnythan

Yeah I'm a bit confused about this.

So when you draw a free-body-diagram for an underwater object, I guess gauge pressure is always ignored*?

It just seemed intuitive that an object that was submerged in water would feel greater pressure.


*I mean yes, when you draw FBDs in the air, you don't take into account pressure of the atmosphere (and air is a fluid, just like water). I guess I shouldn't overthink it with water then...

 

[el_duderino]

What direction would said force be in?

The pressure is equal all around the object. Cancels to zero. Only buoyant force and gravity matter here.

 

[justadream]

@jonnythan

Ok, I see how it cancels out.

But in the first scenario (drain plug), why is gauge pressure relevant? Because it's all in one direction? (going down)?

 

[el_duderino]

Right. There's no water exerting upwards pressure on the other side of the plug. A submerged object experiences the pressure form all directions.