mechanics of fluids Part V

Mechanics of fluids-Part-V : Mechanics of fluids-Part-V By R.Buvana

Mechanism of fluids-part -V : Mechanism of fluids-part -V Surface tension Molecular range and sphere of influence Surface energy Angle of contact Excess pressure inside a liquid drop and a bubble Capillarity Ascent formula

Surface tension : Surface tension Surface tension is a property of a liquid at rest by virtue of which the liquid surface tends to occupy a minimum surface area and behaves like a stretched membrane. T=F/l Units of surface tension is N/m

Molecular range and sphere of influence : Molecular range and sphere of influence The maximum distance up to which the force of attraction between two molecules is appreciable is called molecular range (˜10??m).A sphere with a molecule as centre and radius equal to the molecular range is called the sphere of influence.

Surface energy : Surface energy We know that the molecules on the liquid surface experience net downward force. So to bring a molecule from the interior of the liquid to the free surface, some work is required to be done against the intermolecular force of attraction, which will be stored as potential energy of the molecule on the surface. The potential energy of surface molecules per unit area of the surface is called surface energy. Units of surface energy is J/m??²

Angle of contact : Angle of contact The angle which the tangent to the liquid surface at the point of contact makes with the solid surface inside the liquid is called angle of contact. The angle of contact of mercury with glass about 140° where as the angle of contact of water with glass is about 8°.But for pure water , the angle of contact with glass is taken as 0°.

Excess Pressure inside a liquid drop : Excess Pressure inside a liquid drop Inside a bubble-the force due to surface tension is F=T x 2(2?r) The excess pressure (p-pa) acts on a cross sectional area ?r² of the half of the bubble. F=(p-pa)?r² (p-pa) ?r²=T x 2(2?r) (p-pa)=4T/r Inside the drop-In a drop, there is only one surface (p-pa)=2T/r. Air bubble inside the liquid acts as a drop. Hence excess pressure inside an air bubble in a liquid is given by (p-pa)=2T/r

Capillarity : Capillarity A glass tube of very fine bore throughout the length of the tube is called capillary tube. The phenomenon of rise or fall of liquids in a capillary tube is called capillarity.

Ascent Formula : Ascent Formula 2Tcos ?/r?g=h T-surface tension T-Angle of contact r-radius of tube ?-density of liquid g-acceleration due to gravity h-height of a liquid in a capillary tube.

Home work questions : Home work questions 1.Oil spreads over the surface of water while water does not do so on oil surface. Explain. 2.When two mercury drops are brought into contact, they form one drop. Why? 3.How are small insects able to walk on the water surface? 4.By which phenomenon the water rises from root to leaves of plants?