# How to determine shape of surface of a fluid?

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1. May 11, 2015

### SurajBahuguna

I have been told by my teacher that the surface of a fluid is always perpendicular to the net force acting on it. The reason being a fluid can not withstand tangential stress and if a shear stress is applied to it, it will slip until the surface becomes perendicular to the net force. So my question is why the surface of water is horizontal in a vessl at rest even when the net force acting on it is zero? Also why does it become diagonal(and not vertical) when it is given some horizontal accleration?

2. May 11, 2015

### A.T.

I guess he meant net external force (forces from the fluid itself excluded) acting on the fluid at the surface.

3. May 11, 2015

### Vatsal Sanjay

I differ in perceiving the statement your teacher gave. The surface of the fluid is always perpendicular to the net "external" (actual plus inertial) force acting on the surface in the frame of reference of the container in which it is kept.

4. May 11, 2015

### SurajBahuguna

Thanks for your reply. Does that mean the normal force acting on the fluid due to the container(which is equal in magnitude to the weight of fluid) has to be ignored because it does not have any influence on the surface of the fluid?

5. May 11, 2015

### A.T.

The external forces by the wall influence the shape of the fluid at the wall.

6. May 11, 2015

### Andy Resnick

To the thread title, the shape of a fluid-fluid boundary is given by the Young-Laplace equation ΔP = γ ∇⋅n, that is to say the local curvature is equal to the pressure jump across the interface. This equation can be modified at a three-phase line (generalized theory of capillarity, principally by Neumann).

http://www.crcnetbase.com/doi/abs/10.1201/EBK0849396878-2

Regarding your question about fluid in a bucket, "Newton's bucket" is a delightful problem to consider as it leads, per Mach, directly to general relativity.

7. May 11, 2015

### Staff: Mentor

I guess you are talking about free surfaces here, and moreover, free surfaces over which no air (or other liquid or gas) is blowing. Solid surfaces are certainly able to exert shear stresses on fluids. How else could you have a pressure drop in flow through a tube of constant cross section? Also, if air (or other fluid or gas) is blowing over the free surface, it certainly exerts a shear stress on the fluid at the interface.

Chet

8. May 12, 2015

### officialmanojsh

Agreed!
Example :
If a fluid say water is put in a plastic cup and the cup is squeezed, the shape of fluid changes. Because of the force put by the hand used to squeeze cup. Here the net force of hand and gravity can be considered. :)

9. May 12, 2015

### Staff: Mentor

The external force (per unit area) acting on the free surface of a fluid is not always perpendicular to the surface. Suppose I have a shallow bowl of water filled to the brim, and I put it in a wind tunnel that blows air in the direction tangent to the surface. According to your statement, no water will blow out of the bowl, and the water surface will feel the same force per unit area as if no air were blowing.

Chet

10. May 12, 2015

### Vatsal Sanjay

I agree. You are correct. I will reframe my statement. Whatever I said is true only for fluid statics, that is when there is no relative motion between the container and the fluid kept in it.