Question

Calculate the contact angle $\theta$ for olive oil if capillary action raises it to a height of 7.07 cm in a glass tube with a radius of 0.100 mm. Is this value consistent with that for most organic liquids?

Final Answer

$5.1^\circ$

Most organic fluids have a contact angle with glass of $0^\circ$. The value calculated here is fairly close to zero, and somewhat consistent with the expectation of $0^\circ$.

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 11, Problem 64 (Problems & Exercises)

vote with a rating of
votes with an average rating of
.

### Calculator Screenshots

Video Transcript

This is College Physics Answers with Shaun Dychko. We are going to calculate the contact angle between olive oil and glass and we have a glass tube inserted into some olive oil and the capillary action causes the olive oil to raise up a height of 7.07 centimeters which is 7.07 times 10 to the minus 2 meters and we are told the glass tube has a radius of 0.100 millimeters which is 0.100 times 10 to the minus 3 meters. So we start with this formula which says the height raised due to capillary action is 2 times the surface tension of the fluid times

*cosine*of the contact angle between the fluid and the material of the tube— in this case glass— and we divide by the density of the fluid times gravitational field strength times the radius of the tube. So we are gonna rearrange this for*cos Θ*because we wanna find out what*Θ*is. So we multiply both sides by*ρgr*divided by 2 times*γ*and then switch the sides around as well. So we have*cos Θ*is*ρghr*over 2*γ*and then take the inverse*cos*of both sides and you end up with*Θ*is the inverse*cos*of all this. So we have to look up a lot of information in our data tables. So we have inverse*cos*of the density of olive oil which is 0.92 times 10 to the 3 kilograms per cubic meter multiplied by*g*—9.80 newtons per kilogram— times a height of 7.07 times 10 to the minus 2 meters times the radius of the tube divided by 2 times the surface tension of olive oil— and that is... (where's that... right here) 0.032 newtons per meter— and all this works out to 5.1 degrees is the contact angle between olive oil and glass.