Fluid mechanics

  Expression for capillary rise and capillary fall - Jurin's law Expression for height in Capillary rise Consider a narrow glass tube of diameter of d dipped in a liquid (say water). Water in the tube will rise above the adjacent liquid level. It is called capillary rise. Let σ = Surface tension of liquid. ϴ = Angle of contact between the glass tube and the liquid surface. h = Height of liquid column in glass tube. Under equilibrium, two forces are acting on the water inside. The first one is weight of water column and second is the upward force acting on water due to surface tension. The weight of liquid of height h should be balanced by the force at liquid surface. This force at surface of liquid is due to surface tension. The weight of liquid of height h in the tube = Volume x ρ x g = (π/4)d 2  x h x ρ x g Here ρ = density of liquid g = acceleration due to gravity. The vertical component of surface tensile force = surface tension x circumference x cosϴ = σ x πd x cosϴ At equilib

A liquid of density  ρ ρ  and surface tension  σ σ  rises in a capillary of inner radius  r r  to a height h = 2 σ cos θ ρ g r h = 2 σ cos ⁡ θ ρ g r where  θ θ  is the contact angle made by the liquid meniscus with the capillary’s surface. The liquid rises due to the forces of adhesion, cohesion, and surface tension. If adhesive force (liquid-capillary) is more than the cohesive force (liquid-liquid) then liquid rises as in case of water rise in a glass capillary. In this case, the contact angle is less than 90 deg and the meniscus is concave. If adhesive force is less than the cohesive force then liquid depresses as in case of mercury in a glass capillary. In this case, the contact angle is greater than 90 deg and the meniscus is convex. The formula for capillary rise can be derived by balancing forces on the liquid column. The weight of the liquid ( π r 2 h ρ g π r 2 h ρ g ) is balanced by the upward force due to surface tension ( 2 π r σ cos θ 2 π r σ cos ⁡ θ ). This formula can als

  For a bubble with two surfaces providing tension, the pressure relationship is: This gives

  Surface tension  is the tendency of fluid surfaces to shrink into the minimum surface area possible. Have you noticed when you fill a glass up to the brim with water, you can still add a few more drops till it spills out? Or have you ever broken a thermometer and observed how the fallen mercury behaves? All these happen due to the surface tension of the surface.  Let us understand the concept,  surface tension definition  along with its SI unit, formula and examples. What is Surface Tension? According to the  definition of surface tension , it  is the phenomenon that occurs when the surface of a liquid is in contact with another phase (it can be a liquid as well). Liquids tend to acquire the least surface area possible. The surface of the liquid behaves like an elastic sheet. “Surface tension is the tension of the surface film of a liquid caused by the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimise surface area”. Surface tension no

  Properties of Fluids in Fluid Mechanics   mass density, weight density, specific volume, specific gravity, viscosity. Lets understand these properties of fluids one by one in detail. The knowledge of these properties is very essential to make the study of fluid mechanics comprehensive. The properties of fluids are as follows 1. Density or mass density 2. Specific weight or Weight density 3. Specific volume 4. Specific Gravity 5. Viscosity 1.  Density or Mass Density: It is defined as the ratio of the mass of the fluid to its volume. It is represented by the symbol  ρ (rho). The unit of density is Kg per cubic metre (Kg/m3) The density of liquid is taken as constant while the density of the gases changes with the change in the pressure and temperature .In mathematical form the density is given as   The value of the mass density for the water is 1000 Kg/m3.   2. Specific Weight or Weight Density When the ratio of weight of the fluid to the volume of the fluid is taken out and the quant