JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Excess Pressure

Excess Pressure

Category : JEE Main & Advanced

Due to the property of surface tension a drop or bubble tends to contract and so compresses the matter enclosed. This in turn increases the internal pressure which prevents further contraction and equilibrium is achieved. So in equilibrium the pressure inside a bubble or drop is greater than outside and the difference of pressure between two sides of the liquid surface is called excess pressure. In case of a drop, excess pressure is provided by hydrostatic pressure of the liquid within the drop while in case of bubble the gauge pressure of the gas confined in the bubble provides it.

Excess pressure in different cases is given in the following table :

Plane surface	Concave surface
\[\Delta P=0\]	\[\Delta P=\frac{2T}{R}\]
Convex surface	Drop
\[\Delta P=\frac{2T}{R}\]	\[\Delta P=\frac{2T}{R}\]
Bubble in air	Bubble in liquid
\[\Delta P=\frac{4T}{R}\]	\[\Delta P=\frac{2T}{R}\]
Bubble at depth h below the free surface of liquid of density d	Cylindrical liquid surface
\[\Delta P=\frac{2T}{R}+hdg\]	\[\Delta P=\frac{T}{R}\]
Liquid surface of unequal radii	Liquid film of unequal radii
\[\Delta P=T\left[ \frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}} \right]\]	\[\Delta P=2T\left[ \frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}} \right]\]

Note :

Excess pressure is inversely proportional to the radius of bubble (or drop), i.e., pressure inside a smaller bubble (or drop) is higher than inside a larger bubble (or drop). That is why when two bubbles of different sizes are put in communication with each other, the air will rush from smaller to larger bubble, so that the smaller will shrink while the larger will expand till the smaller bubble reduces to droplet.

JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Excess Pressure

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