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

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 ...

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.

Dimensionless Numbers

Dimensionless Numbers – a vital concept in fluid mechanics , heat transfer , and engineering modeling , especially important for competitive exams like SSC JE , RRB JE , GATE , IES , and various PSUs . 🔢 What Are Dimensionless Numbers? Dimensionless numbers are ratios of quantities that have no physical units. They help compare different physical effects and are essential for modeling, analysis, and similarity in engineering problems. They often arise from the non-dimensionalization of governing equations (like Navier-Stokes or energy equations) and reveal dominant physical forces in a system. 📦 Why Are They Important? Help simplify complex problems Used in model testing (e.g., wind tunnel, hydraulic models) Allow scaling from model to prototype Help determine regimes : laminar vs. turbulent, conduction vs. convection, etc. Appear in correlation equations (e.g., heat transfer coefficients) 📘 Common Dimensionless Numbers (With Physical Me...

Fluid mechanics

Search This Blog