Summary of Mechanical Properties of Fluids
Mechanical Properties of Fluids
Incompressible Fluid: Density remains constant.
Intermolecular Force: Attraction between two molecules.
Cohesive Force: Attraction between molecules of the same substance.
Adhesive Force: Attraction between molecules of different substances.
Range of Molecular Force: Maximum distance from a molecule over which the molecular force is effective.
Sphere of Influence: An imaginary sphere with a molecule at its center, with radius equal to the range of molecular force.
Surface Film: Surface layer of a liquid with thickness equal to the range of intermolecular forces.
Free Surface of Liquid: No shear stress experienced on the surface.
Surface Tension: Tangential force per unit length on either side of an imaginary line on the liquid surface.
Surface Energy: Extra energy of surface layer molecules.
Surface tension of paints & lubricating oils: Kept low to help spread over larger areas.
Formation of Mercury Drops: They combine to minimize surface energy.
Surface Tension & Molecular Theory Explanation: Molecules at the surface experience unbalanced cohesive forces pulling them inside, creating tension.
Relation Between Surface Energy & Surface Tension Derivation: Work done in stretching a soap film relates to its surface energy.
Angle of Contact: Angle between tangents drawn to the liquid’s surface and the solid’s surface. Acute angle forms a concave meniscus; obtuse angle forms a convex meniscus.
Conditions for Angle of Contact:
Zero for pure water which wets the solid entirely.
Ninety degrees when the adhesive and cohesive forces balance.
Shape of Liquid Drops: Described by forces due to surface tension acting on the drop.
Factors Affecting Angle of Contact: Nature of liquid and solid, impurities, temperature.
Effect of Temperature on Surface Tension: Generally decreases with increasing temperature.
Work Done in Forming Soap Bubble: Given by $W = T imes dA$; where $dA$ is the surface area change.
Laplace's Law for Excess Pressure: $Pi - Po = 2T/r$, for spherical membranes.
Capillary Tube: Fine bore tube open at both ends, related to capillarity phenomenon.
Hydrodynamics versus Hydrostatics: Studying properties of fluids in motion vs. at rest.
Viscosity and Newton's Law of Viscosity: Viscosity relates to the drag force between fluid layers, with $f =
u (A)(dv/dx)$.Critical Velocity & Reynolds Number Relationship: $V_c = R n$, classifies flow behaviors based on fluid velocity.
Bernoulli's Principle: Describes conservation of energy in fluid flow.
Pressure Types: Absolute, gauge, and atmospheric pressure defined.
Pascal's Law: Pressure applied to a fluid in a confined space is transmitted undiminished throughout the fluid.