Compressible versus Incompressible Flow

Compressible versus Incompressible Flow

A flow is classified as being compressible or incompressible, depending on the level of variation of density during flow. Incompressibility is an approximation, in which the flow is said to be incompressible if the density remains nearly constant throughout. Therefore, the volume of every portion of fluid remains unchanged over the course of its motion when the flow is approximated as incompressible. The densities of liquids are essentially constant, and thus the flow of liquids is typically incompressible. Therefore, liquids are usually referred to as incompressible substances. A pressure of 210 atm, for example, causes the density of liquid water at 1 atm to change by just 1 percent. Gases, on the other hand, are highly compressible. A pressure change of just 0.01 atm, for example, causes a change of 1 percent in the density of atmospheric air.

Comments

Internal versus External Flow

Internal versus External Flow A fluid flow is classified as being internal or external, depending on whether the fluid flows in a confined space or over a surface. The flow of an unbounded fluid over a surface such as a plate, a wire, or a pipe is external flow. The flow in a pipe or duct is internal flow if the fluid is completely bounded by solid surfaces. Water flow in a pipe, for example, is internal flow, and airflow over a ball or over an exposed pipe during a windy day is external flow (Fig. 1–18). The flow of liquids in a duct is called open-channel flow if the duct is only partially filled with the liquid and there is a free surface. The flows of water in rivers and irrigation ditches are examples of such flows. Internal flows are dominated by the influence of viscosity throughout the flow field. In external flows the viscous effects are limited to boundary layers near solid surfaces and to wake regions downstream of bodies.

Expression for capillary rise and capillary fall - Jurin's law

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 eq...

capillary rise

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 ...

Fluid mechanics

Search This Blog