# Fluid Mechanics and perpendicular force

1. Jan 18, 2014

I was just wondering why a body immersed in a fluid at rest experiences a perpendicular force on its surface? Why cant there be a component of force in parallel direction to the surface ? I read somewhere that this would cause the fluid to flow parallel to the surface but i don't quite understand...can someone please explain.
PS I'm new.

2. Jan 18, 2014

### Staff: Mentor

How does the force know which way to point in the parallel direction?

3. Jan 18, 2014

### bhillyard

Two reasons off the top of my head.
1. If all the forces parallel to the surface were in the same direction (difficult if it is a 3d body) then there would be a net torque on the body and it would rotate. By observation there is no rotation so no nets torque.
2. If the forces parallel to the surface were not in a particular direction relative to the surface what would cause them to be in different directions? The only possibility with regard to the symmetry of the system is if the forces parallel to the surface were zero.

4. Jan 18, 2014

### Staff: Mentor

Nicely analyzed.

Chet

5. Jan 18, 2014

### Malverin

When there is a molecule(atom) of the fluid that touches the body, the forces in all directions are in equilibrium (it is surrounded with the same molecules(atoms)), except the direction to the surface of the body.

So the only unbalanced force will be in direction perpendicular to the surface of the body (forces between fluid and body are not the same as this between fluid molecules)

http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html

Last edited by a moderator: Apr 29, 2017
6. Jan 18, 2014

Makes sense! But why does the force experienced on the surface have to be perpendicular? I can understand if the body immersed is a cube or a cuboid...but what about a body with an inclined edge..like a prism?

Last edited by a moderator: Apr 29, 2017
7. Jan 18, 2014

### Malverin

Because, when fluid molecules are pushed from all sides from their neighbors. The only place they can go, is the volume of the body.
So they press it from all sides.
As I said, in all other directions, there are fluid molecules.
The only direction that molecule get no force from other fluid molecules, is that which points to the body surface.

8. Jan 18, 2014

Yes...I understand..Thanks :)

9. Jan 18, 2014

### Buckleymanor

Gravity it act's in a downwards direction.A fluid surrounding an object which is immersed has gravity acting upon it in that same direction.Gravity does not attract in a parallel direction.

10. Jan 18, 2014

What about the horizontal surfaces of the body? Gravity does explain the force on the vertical surfaces (considering a cube), on the top face. The bottom face force can be explained by buoyancy...but what about the force experienced by the lateral faces (3-D)? I am referring to force perpendicular to the face of course.

11. Jan 18, 2014

### Staff: Mentor

Dear Badfish97. You still haven't answered my question for my earlier post. When you can answer that question, you will know the answer to your question. So, here it is again:

In a static fluid, if there were a force on a surface that is not perpendicular to the surface, the force could be resolved into components perpendicular and tangent to the surface. The tangent component would have a choice of directions within the tangent plane that span 180 degrees. So, if the fluid is static, how would you think that the force would know in what direction it should be pointing within this plane?

As far as your question about fluid forces acting on vertical surfaces is concerned, at a given location in a static fluid, the pressure acts equally in all directions, including horizontally on vertical surfaces. This means that on a surface oriented in any arbitrary direction, the pressure stress always acts normal to the surface. This is an experimentally observed fact that was discovered by Pascal.

Chet

12. Jan 19, 2014

Well if I understood your question correctly, you're asking me the direction of the tangential component of force when it is not perpendicular to the surface. I think that would depend on the direction of the applied force. for eg: (see attachment).

In reference to your explanation, so the surface of the body experiences a force in all direction, but we only consider the normal force acting on it...given this explanation, I'm assuming all the other forces get nullified, so the net force is acting perpendicular to the surface. Am I correct?

PS - Sorry for not replying earlier. I didn't understand your question then.

#### Attached Files:

• ###### Untitled.png
File size:
6.5 KB
Views:
177
13. Jan 19, 2014

### Buckleymanor

The gravitational force on the verticle surfaces is either unbalanced in one direction or another (top or bottom)depeding on the density of the immersed body, or in equilibrium, if it is static within the fluid.
The force acting on the lateral faces is allways equal no matter what the density or the position of the object.

14. Jan 19, 2014

### Staff: Mentor

Unlike a solid, a fluid can't support a tangential component of force at a surface under static conditions. It can if the fluid is shearing (deforming) at the surface (as a result of viscous stresses), but viscous stresses are not present under static conditions (i.e., the fluid is not deforming as time progresses).

No. I should have been more precise in what I said. When a fluid mechanics guy (I'm a fluid mechanics guy with lots of experience) says that the pressure at a point in the fluid acts equally in all directions, what he really means is that, for any arbitrarily oriented surface, the pressure only acts normal to the surface and is the same value irrespective of the orientation of the surface.

In an earlier post, Malverin provided the correct molecular explanation of why, under static conditions, the pressure force in the fluid (pressure stress) only acts perpendicular to the surface.

Chet

15. Jan 20, 2014

### Buckleymanor

What causes the pressure force in the fluid to act perpendicular to the surface.Is it because all the molecules are stacked one on top of another and gravity causes a pressure difference which is greater at the bottom of the container of fluid than the top.
So the pressuire stress points upwards.Or is it some other mechanism which I don't understand.

16. Jan 21, 2014

### Staff: Mentor

It's a combination of two things. Leaving out the molecular explanation, if you analyze the system at the continuum level, then, as you said, the pressure on both sides of a flat horizontal surface must be equal to the weight of the fluid above (plus the atmospheric pressure at the top). In addition to this, there is Pascal's experimental observation that, no matter which direction you orient a flat surface at depth, the pressure force per unit area on it will be normal to the surface and have the same value as when the surface is oriented horizontally. If you used the subsurface pressure to compress a little sphere of fluid, it would compress equally in all directions.

Chet

17. Jan 21, 2014

Given my understanding of vector resolution, the vertical component (Fsinx) of the force should be perpendicular to the horizontal component (Fcosx).I know the slightly delves into a different discussion all together, but plainly, how does resolution of a vector happen then for a static fluid?
i.e. What is the direction of the tangential component of the force?

So, correct me if my understanding is wrong. The reason the surfaces of a body immersed in a fluid
experience a perpendicular force is because the fluid at each point exerts equal pressure in all directions and the only direction where it does not encounter another fluid molecule is towards the surface of the body. Since it is surrounded by other fluid molecules in all directions except the surface and the shortest distance between the molecule in question and the surface is in the perpendicular direction, and since it is the only direction where it will encounter an unbalanced force, it exerts pressure perpendicular to the surface........?

18. Jan 21, 2014

### Staff: Mentor

The momenta of the individual molecules striking the surface are in all different directions. However, the tangential components of the momenta all cancel each other out (statistically) if the fluid is static. But the normal components do not cancel each other out. This gives rise to a pressure force per unit area on the surface acting normal to the surface only.