Surface tension and force on water between glasses

[Dinheiro]

Homework Statement

I need help on understanding a little part of the solution to this problem I've found on the internet.
The problem

Homework Equations

Surface tension and pressure equations

The Attempt at a Solution

The solution

My doubt:
"The other component of the curvature is negligible because D>>d" What component? Did it mean the part in contact with the glass? Wouldn't the glass' weight interfeer the pressure?

By the way, can someone demonstrate me the young's equation of pressure on curved surfaces? I would really appreciate the help, Thanks.

 

[Chestermiller]

Homework Statement

I need help on understanding a little part of the solution to this problem I've found on the internet.
The problem

View attachment 72108

Homework Equations

Surface tension and pressure equations

The Attempt at a Solution

The solution

View attachment 72109

My doubt:
"The other component of the curvature is negligible because D>>d" What component? Did it mean the part in contact with the glass? Wouldn't the glass' weight interfeer the pressure?

There are two principal contributions to the pressure difference between the water inside and the air outside. The problem already discussed one of these. The other is the hoop tension, which acts like a belt around the disk of liquid. This is also caused by the surface tension, and contributes a pressure increase equal to 2γ/D (it's like, when you tighten your belt, the pressure gets higher on your belly). But note that this is much lower than 2γ/d.

The problem inherently neglects the weight of the glass.

Chet

 

[Dinheiro]

Thanks, Chet!