Find Force exerted on Sphere.

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1. Mar 25, 2016

LoveBoy

1. The problem statement, all variables and given/known data

2. Relevant equations
What is gauge pressure ?

3. The attempt at a solution

How to find gauge pressure ?

2. Mar 25, 2016

LoveBoy

3. Mar 25, 2016

Nathanael

Gauge pressure is the true pressure minus the ambient air pressure. It can be thought of as "the pressure difference compared to the surface of the liquid." (It is zero at the surface of a liquid. ) Maybe another way to say it is that it is the pressure due only to the weight of the liquid (as opposed to the liquid+atmosphere).

It doesn't make sense to me why they said "Find the force (...) due to gauge pressure" because all of the answers involve the atmospheric pressure... so they are obviously not using the gauge pressure.

I would say just pretend it says "pressure" in place of "gauge pressure."

4. Mar 25, 2016

LoveBoy

Can you please give me some more hint ?

5. Mar 25, 2016

Nathanael

I don't want to hint at it too much before you attempt the problem, but I will say this much:

There are two approaches (that I see), the messy approach and the neat approach. The messy approach involves integrating the pressure over the surface area. The neat approach involves using archimedes principle in a clever way. I will let you contemplate on how to use archimedes principle to solve this problem. (The less hints I give the more satisfying it will be to solve!)

6. Mar 26, 2016

LoveBoy

Well , i'm sorry , i can't calculate the answer yet.

7. Mar 26, 2016

ehild

Cut the sphere into halves, and remove the bottom half. Consider the forces acting on the upper half sphere . The force Fb acting at he base is upward, and there is the downward force Fs on the upper half spherical surface. The result of these forces is the buoyant force, B. You can determine Fb and B, so you get Fs.

8. Mar 27, 2016

LoveBoy

Am i right till here ?

9. Mar 27, 2016

ehild

Not yet. What is V?
Fb is the force exerted by the fluid on the base of the semiphere. It is equal to the hydrostatic pressure at the position of the base multiplied by the area of the base. At what depth is the base of the semiphere? What is the hydrostatic pressure there?
B is the buoyant force - it is equal to the weight of the fluid displaced.How much is it?

10. Mar 27, 2016

LoveBoy

By the way,i'm confused in finding the buoyant force i.e weight of fluid displaced .

11. Mar 27, 2016

ehild

In my notation, Fb is the force exerted by the fluid at the base of the upper hemisphere. It is equal to the pressure at that depth multiplied by the area of the hemisphere. The radius of the sphere is r, what is that area then? And what is Fb?

Do you know Archimedes' principle? The buoyant force B is equal to the weight of the fluid displaced by the upper hemisphere. There is no fluid at the place of the hemisphere, so the volume of the displaced fluid is equal with the volume of the hemisphere. If you know the volume and the density, you can get the weight, don't you?

Last edited: Mar 27, 2016
12. Mar 27, 2016

LoveBoy

Am i right now ?

13. Mar 28, 2016

ehild

The pressure at a depth is proportional to the depth. The base is at depth of 3r. What is the hydrostatic pressure then?
The pressure in the fluid depends also on the atmospheric pressure Po. The pressure adds to the pressure of the fluid, so the pressure at the base is Po+3rρg. The force exerted on a plane surface of area A is independent of direction of the surface. It is the same upward or downward or sideways.

It is correct that the volume of the displaced fluid is (2/3)πr3, but the weight of the fluid is the volume multiplied by the density of the fluid and g .
The buoyant force comes from the difference of the upward force, acting at the base of the hemisphere and the downward force exerted on the spherical surface.

14. Mar 28, 2016

LoveBoy

Is it correct ?

15. Mar 28, 2016

ehild

Your notations are completely different from my ones. Is B the force on the spherical surface? And is Fb the buoyant force? And is Fs the force on the base of the hemisphere? If yes, you are right. What do you get for B?

16. Mar 28, 2016

LoveBoy

Thanks a lot @ehild !