**
***When we place a straw (a hollow cylindrical tube) in water, the water inside the straw rises above the surface level outside and a miniscus (curvature of the surface) forms. Consider the column of water in the straw from the height of the water outside the straw to the top of the column. (See figure, where the column is shown shaded.) Let P _{1} be a point in the straw at the bottom of the column and let P_{2} be a point inside the water column at the top.*

*The force due to surface tension for a maximally stretched surface is given by F _{surf} =γL*

*, where*

*γ*

*is the coefficient of surface tension (which depends only on the substance) and L is the length of the line of contact between an object and the fluid. For this problem use the following:*

*ρ** **= density of water*

*γ** **= surface tension of water*

*r** **= radius of the straw*

*h** **= height of the column*

*P _{atm}*

*= atmospheric pressure*

*g** **= acceleration due to gravity*

* *

*What expression approximates the force due to surface tension? *