Surface Tension: Pressure Diff & Cross-Sectional Area Explained

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SUMMARY

The discussion clarifies the relationship between pressure difference, surface tension, and cross-sectional area in droplets. It establishes that when calculating the force due to surface tension, the pressure difference is multiplied by the cross-sectional area rather than the total surface area. This is because the pressure acts perpendicular to the surface, and integrating the normal component over the surface yields the same result as using the cross-sectional area. The explanation also extends to bubbles, reinforcing the same principles.

PREREQUISITES
  • Understanding of basic fluid mechanics concepts
  • Familiarity with surface tension principles
  • Knowledge of pressure differentials in fluids
  • Basic calculus for integration of forces over surfaces
NEXT STEPS
  • Research the mathematical derivation of surface tension forces in droplets
  • Explore the concept of pressure difference in spherical geometries
  • Study the behavior of bubbles and their surface tension dynamics
  • Learn about applications of surface tension in various fluid systems
USEFUL FOR

Students and professionals in physics, fluid mechanics, and engineering, particularly those interested in the behavior of liquids and gases under varying pressure conditions.

KishoreAM
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Hi Guys...
I have a small doubt regarding surface tension.
When calculating the relation between Pressure Difference inside and outside a Droplet and Surface Tension, we multiply Pressure Difference with Cross Sectional Area of the Droplet and equate it to the Surface tension force.
My doubt is "Why do we use Cross Sectional Area, but not Total Surface Area of the Droplet?" (Pressure acts over the whole surface)
Please Explain the "Bubble" too
 
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KishoreAM said:
Hi Guys...
I have a small doubt regarding surface tension.
When calculating the relation between Pressure Difference inside and outside a Droplet and Surface Tension, we multiply Pressure Difference with Cross Sectional Area of the Droplet and equate it to the Surface tension force.
My doubt is "Why do we use Cross Sectional Area, but not Total Surface Area of the Droplet?" (Pressure acts over the whole surface)
Please Explain the "Bubble" too
The pressure acts perpendicular to the surface of the drop. If you determine its component normal to the cross section of interest and integrate that over the surface of the drop, the result is just the pressure times the cross sectional area.
 

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