Is the pressure at points P1 and P2 the same in surface tension controversy?

  • Context: Undergrad 
  • Thread starter Thread starter i_island0
  • Start date Start date
  • Tags Tags
    Surface
Click For Summary

Discussion Overview

The discussion revolves around the pressure differences at two points, P1 and P2, within a liquid exhibiting capillary rise and surface tension effects. Participants explore the implications of these pressures on the shape of the meniscus and the role of surface tension in determining pressure calculations.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether pressures P1 and P2 are the same or different, linking this to the shape of the meniscus and the pressures at points P1' and P2'.
  • Another participant suggests that the reasoning may be flawed if the calculation of P1' and P2' neglects the effects of surface tension.
  • It is argued that surface tension plays a significant role in the equilibrium of the liquid system, affecting the overall energy and pressure distribution.
  • One participant emphasizes that their pressure equation only accounts for gravitational potential energy, potentially overlooking the influence of surface tension.
  • A suggestion is made to analyze the meniscus shape as a problem of variation calculus, indicating that literature or numerical simulations could provide insights.
  • Another participant expresses confusion regarding the correct equation to use for pressure calculations in this context.
  • There is a statement indicating that the curvature of the meniscus should not necessarily be hemispherical, reflecting uncertainty about the meniscus shape.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether pressures P1 and P2 are the same or different, and there is ongoing debate regarding the role of surface tension in pressure calculations and meniscus shape.

Contextual Notes

Participants express uncertainty regarding the correct equations to use for calculating pressures in the presence of surface tension, and there are unresolved questions about the implications of these calculations on the shape of the meniscus.

i_island0
Messages
123
Reaction score
0
We know about capillary rise. And we say that meniscus is hemispherical in shape.
Now please see this picture.
http://www.flickr.com/photos/63184961@N00/3030969897/

There i am mentioning two points where the pressure is indicated as P1 and P2.
I am also mentioning two other points 1' and 2'. the pressure there is atmospheric (Po).
Are these pressure P1 and P2 same or different.
If same, then pressure P1' and p2' will be different owing to different heights h1 and h2. But we know that P1' = Po and P2' = Po.
If different, then how can the shape of meniscus be hemispherical. It must be flat then.
Where am i going wrong??
 
Physics news on Phys.org
i_island0 said:
Are these pressure P1 and P2 same or different.
If same, then pressure P1' and p2' will be different owing to different heights h1 and h2.

The flaw in your reasoning lies here. I suspect you are calculating P1' and P2' by using an equation that neglects surface tension? If so, you're ignoring the effect that you want to study.
 
Mapes said:
The flaw in your reasoning lies here. I suspect you are calculating P1' and P2' by using an equation that neglects surface tension? If so, you're ignoring the effect that you want to study.

Surface tension is a surface phenomenon. So when i am inside the liquid, surface tension has no role to play.
I am using P = Po + dgh (d: density of liquid) to find the pressure. So where is the flaw?
 
i_island0 said:
So when i am inside the liquid, surface tension has no role to play.

Sure it does. Any portion of the liquid will move to reduce the total energy of the system; this is the meaning of equilibrium. Surface energy affects the entire system.

Your equation for pressure only includes potential energy changes related to gravity, not surface tension, so it predicts a flow from 2' to 1' because of a pressure difference. It neglects the fact that this flow would rearrange the surface profile to be flatter, which would result in a net energy penalty.
 
Mapes said:
Your equation for pressure only includes potential energy changes related to gravity, not surface tension, so it predicts a flow from 2' to 1' because of a pressure difference. It neglects the fact that this flow would rearrange the surface profile to be flatter, which would result in a net energy penalty.

So can you please tell me what should be the correct equation then. As i m really confused about all this.
 
Analytically, the meniscus shape looks like a problem for variation calculus: find the curve that minimizes total system energy. There may be some literature out there on this problem, but I don't know. You could also solve it numerically through simulation. Hopefully someone with more fluids experience can weigh in.
 
thx.. i wish some one can reply on this. AS far as i understand, the curvature of meniscus should not be hemispherical.
 

Similar threads

Undergrad Proving Torricelli's Law Using Bernoulli's Principle
  • · Replies 20 ·
Replies
20
Views
4K
Doublet flow in Fluid Dynamics between two spheres or cylinders
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Bernoulli's Equation Applied to Two Free Surfaces
  • · Replies 34 ·
2
Replies
34
Views
7K
High School Confusion when considering pV=nRT in Two Balloon experiment
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Irreversible adiabatic processes & entropy change (clarification needed)
  • · Replies 22 ·
Replies
22
Views
6K
Pressure Calculations at Points A and B using Pascal's Paradox
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Pressure variation across streamlines in a free jet
  • · Replies 25 ·
Replies
25
Views
7K
Undergrad Why are liquid surfaces at constant pressure?
  • · Replies 2 ·
Replies
2
Views
2K
Calculating Pressure Difference in an Equilibrium Hydrostatics System
  • · Replies 2 ·
Replies
2
Views
2K
Measuring Height of Meniscus in Capillary Action
  • · Replies 1 ·
Replies
1
Views
4K