# Surface Tension

The molecules in the middle of a fluid exert an attractive force on each other, called cohesion. This is what holds the fluid together. The molecules at the surface of the fluid, however, experience a cohesive force directed into the fluid. If the surface becomes bent for some reason, there is a restoring force making the surface smooth or flat. The larger the distortion, the larger the force, up to a maximum:F_{max} = Î³L |
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*Î³*is the surface tension (a function of the fluid) and

*L*is the length of the edge of the object in contact with the fluid. This will become clearer with some examples.

Water has a surface tension of 7.2 x 10^{â€“2} N/m at 25Ëš C. A six-legged water bug stands on the surface of the water. The radius of each foot is 2 x 10^{â€“4 }m. What is the maximum force on the bug due to the water? That is, what is the maximum weight the water surface tension can support?

In this case, *L* is the circumference of a foot. (See Figure 10-7.) Applying the formula yields

*F*_{max} = 6*Î³* (2*Ï€**r*) = 5 x 10^{â€“4} N, where 6 is the number of legs on the bug.

**Figure 10-7**

A needle floats on the surface of the water as shown in Figure 10-8. Its length is *l* = 3 cm, and its width is very small. What is the maximum force exerted on the needle by the surface tension of the water?

**Figure 10-8**

In this case, *L* is the circumference of the dimple, that is, the length of distorted surface around the needle or the length of the dashed line in Figure 10-8. Notice the similarity between Figures 10-7 and 10-8. We use the formula for the perimeter of a rectangle:

L = 2*l* + 2*w* â‰ˆ 2*l*

since the width w is very small. Thus we have

F_{max} = *Î³*(2*l*) = 4.3 x 10^{â€“3} N

A straight piece of wire has loops at both ends, and the two hoops fit on the arms of a U-shaped frame. A water film fills the interior of the U-shape. (See Figure 10-9.) In this case the surface tension exerts its maximum force.

If the length of the wire is *l* and the width of the film is *w*, what is the force of surface tension?

**Figure 10-9**

The circumference is the distance around the wire, as in the previous example. In Figure 10-9 we measure the length of the wire along the front of the page and then along the back of the page:

*F*_{max} = Î³(2*l*)