Hydrostatic forces on a submerged curved surface question

[abuh11]

Hi, i would like to know how to do this question for fluid mechanics. Sorry as I am new i didnt know how to upload images so i just uploaded the image in justpaste, here is the link http://justpaste.it/pz7r

 

[theodoros.mihos]

May you know a pressure definition like $P=\frac{F}{A}$.
You can use it as $dF = P\,dA$ with direction vertical to surface.

 

[Chestermiller]

May you know a pressure definition like $P=\frac{F}{A}$.
You can use it as $dF = P\,dA$ with direction vertical to surface.

I think what you mean is "perpendicular to the surface" rather than "vertical to the surface." Abuh11, to elaborate, the pressure at any depth is acting in the direction perpendicular to the surface. So you need to determine the pressure at each depth, multiply by the differential area involved, and add the forces vectorially (i.e., integrate over the arc of the surface).

 

[abuh11]

I think what you mean is "perpendicular to the surface" rather than "vertical to the surface." Abuh11, to elaborate, the pressure at any depth is acting in the direction perpendicular to the surface. So you need to determine the pressure at each depth, multiply by the differential area involved, and add the forces vectorially (i.e., integrate over the arc of the surface).

Thanks for your reply, what I normally do is use F = pgha to find horizontal component of the force, then use F = phv to find vertical component forces, then I find out the actual force using F^2 = FH^2 + FV^2. However the problem I’m having is finding the vertical component as I don’t know how to calculate the volume of the water that the shape is occupying. I normally work with questions in which the curved surface is fully submerged whereas here it is only partially submerged. The correct answer is meant to be 52050N although I’m not getting it with my current calculations.

 

[Chestermiller]

There's another way to do this. Do you know how to calculate the weight of the part of the water sitting directly above the gate?

 

[abuh11]

There's another way to do this. Do you know how to calculate the weight of the part of the water sitting directly above the gate?

no

 

[Chestermiller]

no

Do you know how to find the volume of this water using geometry or calculus?

 

[abuh11]

Do you know how to find the volume of this water using geometry or calculus?

I used geometry but not calculus

 

[Chestermiller]

I used geometry but not calculus

OK. From geometry, what is the volume of water directly under the gate.

 

[abuh11]

There's another way to do this. Do you know how to calculate the weight of the part of the water sitting directly above the gate?

That is part of the problem, i know how to do this for when the curved surfaces is fully submerged, but for this type of question i don't know how to do it.

 

[Chestermiller]

That is part of the problem, i know how to do this for when the curved surfaces is fully submerged, but for this type of question i don't know how to do it.

I asked you for the volume of liquid below the gate. This is a geometry question, not a physics question. This is just the first step in getting to the answer you want. If you 're not willing to be patient, I won't be able to help you. This is part of how we determine the vertical component of force on the gate.

 

[abuh11]

I asked you for the volume of liquid below the gate. This is a geometry question, not a physics question. This is just the first step in getting to the answer you want. If you 're not willing to be patient, I won't be able to help you. This is part of how we determine the vertical component of force on the gate.

i don't know how to do that for this type of question.

 

[insightful]

Hint: Find area A, then area B.

 

[abuh11]

Hint: Find area A, then area B.

Interesting, i see where you are going with this, but how would you find the area of B.

 

[Chestermiller]

You find A +B and subtract A to get B

 

[abuh11]

You find A +B and subtract A to get B

Ok, i done that. I got A and B now, what should i do with these numbers now?

 

[insightful]

Ok, i done that. I got A and B now, what should i do with these numbers now?

Area B can get you to the volume of water displaced, right?

 

[abuh11]

Area B can get you to the volume of water displaced, right?

How would you find the area of the shape above A, I am asking as i tried subtracting A from the area of the entire semi circle, but in order to find B we need to take into account the area above/next to A.

 

[insightful]

...in order to find B we need to take into account the area above/next to A.

Not really. What are the angles of triangle A? What is the area of the sector of the circle (A+B)?

 

[abuh11]

Not really. What are the angles of triangle A? What is the area of the sector of the circle (A+B)?

I don't think we know the angles of A.

 

[insightful]

I don't think we know the angles of A.

Hmm...a right triangle with two of the sides known...you've had trigonometry, right?

 

[abuh11]

Hmm...a right triangle with two of the sides known...you've had trigonometry, right?

yay. I manged to figure it out using your diagram and information. Thanks a lot.

 

[insightful]

yay. I manged to figure it out using your diagram and information. Thanks a lot.

An interesting problem; I enjoyed working on it.

 

[insightful]

I like problems with obvious real-world application:

https://en.wikipedia.org/wiki/Tainter_gate

 

[abuh11]

I like problems with obvious real-world application:

https://en.wikipedia.org/wiki/Tainter_gate

Yeah this question was actually one question from a exam for my course, I am studying civil engineering (one of benefits as you mentioned is that the math is applied).