Fluid mechanics for GATE exam 2017

GATE is an all India examination administered under the expert guidance of IISC, Bangalore and seven IITS every year to test the aptitude of students in different branches of engineering. The exam is the guaranteed ticket to a secured and bright future as getting through the exam with satisfying scores and good ranks offers them the opportunity of pursuing post graduate programmers from elite institutions of the county along with a fat pay scale job with distinctive public sector undertakings. For session 2017-18, the official notification has been released on its official site and this year, the exam will be conducted by IIT, Roorkee. So, it’s high time you should start preparing for the exam. Fluid mechanics is an important section for mechanical engineering domain. Our team of experts has made notes on an important subtopic of this section. Go through it to clear the concept and practice question over the same to reinstate your knowledge of the concept.

Surface Tension and Capillary Effect

Consider two liquid molecules, one deep within the liquid body (A) and one at the surface (B).

The attractive forces applied on molecule A balance each other because of symmetry. But the attractive force acting on the surface molecules are not symmetric. The molecule is under the influence of net downward force. The net inward force at B depends only on the attraction of molecules inside the liquid but also on attraction by the molecules of air on the other side of surface. Attractive forces applied by the gas molecules above are very small and hence can be neglected. Hence work is done on each molecule arriving at the surface against the action of inward force. Thus mechanical work is done is performed in creating a free surface or increase the area of surface. Therefore existence of free surface implies the presence of stored mechanical energy known as free surface energy.

 

Any system tries to attend the condition of stable equilibrium with its potential energy as minimum. Liquid droplets will adjust its shape until its surface area and consequently free surface energy is minimum. Drop of liquid takes spherical shape which has minimum surface area for a given volume.

 

A curved surface indicates a pressure difference across the interface with pressure being higher on concave side. Consider, for example, a droplet of liquid in air or an air bubble in water. The excess pressure  above atmospheric pressure tries to burst the droplet of liquid and increase the surface area whereas surface tension developed in stretched elastic surface (membrane) tries to minimize the surface area. The resisting tension force per unit length developed on the surface is called surface tension.

 

Equilibrium condition for a liquid droplet is obtained by balancing the forces on both sides considering a projected area of half sphere

The surface tension force varies greatly from substance to substance and with temperature for a given substance. At 200C the surface tension is 0.073 N/m for water and 0.44 N/m for mercury surrounded by atmospheric air. Surface tension determines the size of the liquid droplets that form, and so a droplet keeps growing by the addition of more mass, breaks down when the surface tension is no longer able to hold it together.

Hollow bubble like soap in air has two surfaces in contact with air, one inside and other outside. Thus two surfaces are subjected to surface tension. The equilibrium condition becomes

Capillarity

is defined as rise or fall of a liquid surface in a small tube relative to adjacent level of liquid when the tube is held vertically in the liquid.

 

It is observed that water in glass container curves up slightly at the edges where it touches the glass surface and mercury in glass container curves down slightly where it touches the glass surface. The liquid molecules at the solid liquid interface are subjected to both cohesive forces by other liquid molecules and adhesive forces by the molecules of solid. In case of water adhesive forces dominate over cohesive forces and thus water tends to rise along the glass surface. The opposite occurs for mercury, which causes the liquid surface near the glass wall to be suppressed.

 

Contact angle is the angle that the tangent to the liquid surface makes with the solid surface at the point of contact. When the contact angle () is less than 900 we say the liquid wets the surface and when is more than 900 the liquid do not wet the surface.