Max Height of Water in a Container with 0.1mm Hole: Solving h

[erisedk]

Homework Statement

A container has a round hole at the bottom. The diameter of the hole is 0.1 mm. The container is filled with water. The maximum height (in m) up to which whiter can be filled without leakage is h/10. Find h.
Surface tension= 75 * 10^-3 N/m

Homework Equations

Pgh*A=F(of surface tension)

The Attempt at a Solution

Weight of water on the hole should equal force of surface tension.
Pgh*pi*r^2=T*2*2*pi*r

solving for h, I get h=6. However, the answer is 3. Does this mean that force of surface tension is not equal to 2*(T*2*pi*r) and instead is just equal to (T*2*pi*r)? However, isn't force of surface tension T*two times the length in contact??

 

[Chestermiller]

Homework Statement

A container has a round hole at the bottom. The diameter of the hole is 0.1 mm. The container is filled with water. The maximum height (in m) up to which whiter can be filled without leakage is h/10. Find h.
Surface tension= 75 * 10^-3 N/m

Homework Equations

Pgh*A=F(of surface tension)

The Attempt at a Solution

Weight of water on the hole should equal force of surface tension.
Pgh*pi*r^2=T*2*2*pi*r

solving for h, I get h=6. However, the answer is 3. Does this mean that force of surface tension is not equal to 2*(T*2*pi*r) and instead is just equal to (T*2*pi*r)? However, isn't force of surface tension T*two times the length in contact??

Only if it is a bubble, which has two surfaces. The drop has only one surface, so there is no 2.

Chet

 

[erisedk]

Oh ok! Thanks :D

 

[member 428835]

Sorry for chiming in here late, but if $\rho g h A = F_{ST}$ it appears that surface tension always acts normal to the surface under study? Is this true?

 

[Bystander]

surface tension always acts normal to the surface

That's one guess. There's only one other possibility.

 

[member 428835]

That's one guess. There's only one other possibility.

haha okay, so I'm wrong then?

 

[Bystander]

Have you read the threads shown in the search?

 

[member 428835]

yea, i have read some of them but have been busy. i can check more out, though.

 

[member 428835]

I don't think I've been lazy here, I'm just waiting for confirmation. See, I have $A = xy$ and $g = z / s^2$ and $h = z$ and $\rho = kg / xyz$. this implies $$\frac{[kg] [x] [y] [z^2]}{[s^2] [x][y][z]} = \frac{[kg][ z]}{[s^2]}$$ hence the $z$ remains. It then seems that the surface tension force is normal to the surface. However, since surface tension is force per unit length, I'm confused if the length is $x$ or $y$, since, in this example, the two are symmetric.

 

[Bystander]

ρghA=F ST

This describes the balance of forces for a capillary rise experiment which is one method used to determine surface tension. Which directions do the forces act in the case of capillary rise?

 

[member 428835]

I edited my response, I'm not sure if the edit went through in time for your response. And I'm not sure about directions for capillary rise. Could you elaborate, or help me understand?

 

[Chestermiller]

Sorry for chiming in here late, but if $\rho g h A = F_{ST}$ it appears that surface tension always acts normal to the surface under study? Is this true?

The right hand side of this equation should be a length times the surface tension. Think of surface tension as a membrane stretched over the surface. The tension per unit length within the membrane is the surface tension.

Chet

 

[Bystander]

If you immerse one end of a capillary (think soda straw) in a container of some liquid you will for most cases observe a difference between the height of the meniscus formed by the liquid in the capillary and the surface of the liquid in the container. That difference is due to the surface tension of the liquid as it either wets or does not wet the interior surface of the capillary. Got that pictured?

 

[member 428835]

Bystander, I can picture that.

And Chet, it sounds like there is never a preferred direction, but that surface tension is in the direction to deflect a perturbation within a fluid?

 

[Chestermiller]

Bystander, I can picture that.

And Chet, it sounds like there is never a preferred direction, but that surface tension is in the direction to deflect a perturbation within a fluid?

If I inderstand correctly, yes.

 

[member 428835]

Thanks Chet!

 

[haruspex]

surface tension is in the direction to deflect a perturbation within a fluid?

Not sure what you mean by that. At a boundary, it acts within its surface, normal to the boundary with the other surface.

If you immerse one end of a capillary (think soda straw) in a container of some liquid you will for most cases observe a difference between the height of the meniscus formed by the liquid in the capillary and the surface of the liquid in the container.

By height of meniscus, are you referring to the level of the meniscus in the tube above the liquid outside the tube, or (entirely within the tube) the level of the line of contact with the tube above the level of the surface in the middle of the tube?
If the second, I believe it is not so much to with the air/liquid surface tension as to do with how the cohesive forces within the liquid compare with the adhesive forces between liquid and tube.

 

[Bystander]

compare with the adhesive forces between liquid and tube.

"Wetting" and contact angles? Nah, let's not go there --- reasonably well designed lab exercises drag students through everything short of piranha solution to clean their capillaries well enough to get "perfect" wetting and a zero contact angle --- which reduces to air-liquid interface tension.