Hydrostatic forces on a submerged curved surface question

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The discussion focuses on solving a fluid mechanics problem involving hydrostatic forces on a partially submerged curved surface. Participants clarify the definition of pressure and its application in calculating forces acting on the surface. A key challenge is determining the volume of water above the gate to find the vertical component of the force, which differs from fully submerged scenarios. Geometry is emphasized as a crucial tool for calculating the volume and area needed for the solution. Ultimately, the problem is resolved through collaboration and application of trigonometric principles.
abuh11
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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
 
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May you know a pressure definition like ##P=\frac{F}{A}##.
You can use it as ##dF = P\,dA## with direction vertical to surface.
 
theodoros.mihos said:
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).
 
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Chestermiller said:
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.
 
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?
 
Chestermiller said:
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
 
abuh11 said:
no
Do you know how to find the volume of this water using geometry or calculus?
 
Chestermiller said:
Do you know how to find the volume of this water using geometry or calculus?

I used geometry but not calculus
 
abuh11 said:
I used geometry but not calculus
OK. From geometry, what is the volume of water directly under the gate.
 
  • #10
Chestermiller said:
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.
 
  • #11
abuh11 said:
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.
 
  • #12
Chestermiller said:
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.
 
  • #13
Hint: Find area A, then area B.
 

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  • #14
insightful said:
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.
 
  • #15
You find A +B and subtract A to get B
 
  • #16
Chestermiller said:
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?
 
  • #17
abuh11 said:
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?
 
  • #18
insightful said:
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.
 
  • #19
abuh11 said:
...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)?
 
  • #20
insightful said:
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.
 
  • #21
abuh11 said:
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?
 
  • #22
insightful said:
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.
 
  • #23
abuh11 said:
yay. I manged to figure it out using your diagram and information. Thanks a lot.
An interesting problem; I enjoyed working on it.
 
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  • #25
insightful said:
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).
 

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