Fluid mechanics

• Cohesion means intermolecular attraction between molecules of the same liquid.
• Adhesion means attraction between the molecules of a liquid and the molecules of a solid boundary surface in contact with the liquid.
• Capillary action is due to both cohesion and adhesion.
• Surface Tension is defined as the tensile force acting in the surface of a liquid in contact with a gas or on the surface between two immiscible liquid such that the contact surface between is like a membrane and tension.
• Surface Tension is caused by the force of cohesion as at the free surface.
• Examples of phenomenon of surface tension include the rise of the sap in the tree, collection of dust particles in water surface, break up of liquid jets, and the formation of rain drops.
• Surface Tension is expressed in (unit:) N/m.
• The characteristic equation of a state of a perfect gas, PV = MRT, is used for this purpose.
• The equivalent depth of water to a certain depth of oil can be calculated using the formula ρg = ρo (1 - r).
• The thermodynamic properties need to be considered when a fluid is influenced by change of temperature.
• In a steady (ordered) flow, Poiseuille stated that the volume flowing per second depends on the viscosity, the radius r of the pipe and the pressure gradient, P/L.
• The pressure inside a water droplet, soap bubbles and a liquid jet can be determined using surface tension.
• An air bubbles has only one surface.
• Viscosity of fluids is due to cohesion and interaction between particles.
• The constant of proportionality in Newton’s law of Viscosity is called the coefficient of viscosity.
• Water, kerosene, and air are examples of Newtonian fluids.
• The capillary rise is calculated by subtracting the surface tension from the height of the liquid in the tube.
• The minimum size of glass tubing that can be used to measure water level is determined by the capillary rise, which is the maximum height of the liquid in the tube.
• The viscosity of the fluid between the plates can be calculated using Newton’s law of Viscosity.
• The capillary depression is calculated by subtracting the surface tension from the height of the liquid in the tube.
• Viscosity may be defined as the property of a field which determines its resistance to shearing stresses.
• Newton’s law of Viscosity states that the shear stress on a fluid element layer is directly proportional to the rate of shear strain.
• The level of the liquid in a tube relative to the free surface of the liquid inside the tube is determined by the capillary depression, which is the negative of the height of the liquid in the tube.
• The work done = total energy change W = Δ P.E + Δ K.E ( P 1 - P 2) V = ½ ρ V (v 2 2 - v 1 2) + ρ Vg (h 2 - h 1) ( P 1 - P 2) = ½ ρ ( v 2 2 - v 1 2) + ρ g (h 2 - h 1) P 1 + ½ ρ v 1 2 + ρ gh 1 = P 2 + ½ ρ v 2 2 + ρ gh 2 (Bernoulli’s equation)
• The work done in moving volume, V of fluid from section 1 of pipe to section 2 is given as: W = (P 1 - P 2) V.
• ρ = m/V ⇒ m = ρ V.