# Hydrostatic forces on a submerged curved surface question

1. Dec 27, 2015

### abuh11

• No template because of misplaced homework
Hi, i would like to know how to do this question for fluid mechanics. Sorry as im new i didnt know how to upload images so i just uploaded the image in justpaste, here is the link http://justpaste.it/pz7r

2. Dec 27, 2015

### 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.

3. Dec 29, 2015

### Staff: Mentor

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).

4. Dec 29, 2015

### abuh11

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.

5. Dec 29, 2015

### Staff: Mentor

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?

6. Dec 29, 2015

### abuh11

no

7. Dec 29, 2015

### Staff: Mentor

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

8. Dec 29, 2015

### abuh11

I used geometry but not calculus

9. Dec 29, 2015

### Staff: Mentor

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

10. Dec 29, 2015

### abuh11

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 dont know how to do it.

11. Dec 29, 2015

### Staff: Mentor

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. Dec 29, 2015

### abuh11

i dont know how to do that for this type of question.

13. Dec 29, 2015

### insightful

Hint: Find area A, then area B.

#### Attached Files:

• ###### Gate.jpg
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14. Dec 29, 2015

### abuh11

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

15. Dec 29, 2015

### Staff: Mentor

You find A +B and subtract A to get B

16. Dec 29, 2015

### abuh11

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

17. Dec 29, 2015

### insightful

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

18. Dec 29, 2015

### abuh11

How would you find the area of the shape above A, im 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. Dec 29, 2015

### insightful

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

20. Dec 29, 2015

### abuh11

I dont think we know the angles of A.