Introduction to Fluid Mechanics and Momentum Transfer

Scope and Objectives

Fluid mechanics is a foundational subject in chemical and process engineering, focusing on the behavior of fluids (liquids, gases, and vapors) and the forces acting upon them. Momentum transfer, often referred to as "fluid mechanics," is essential for understanding how fluids move and interact with their surroundings.

• Objective 1: Explain the scope of fluid mechanics and distinguish between fluid statics and dynamics.

• Objective 2: Define and explain fluid pressure, hydrostatic force, and pressure head.

• Objective 3: Analyze hydrostatic force on submerged surfaces.

• Objective 4: Analyze different types of manometers and pressure differences in connected fluid columns.

Momentum Transfer: Definition and Scope

Definition of Momentum Transfer

Momentum transfer is the branch of engineering science that deals with the behavior and movement of fluids (liquids, gases, and vapors). It is also known as fluid mechanics.

• Fluid Mechanics is divided into two main areas:

  • Fluid Statics: Study of fluids at rest (no shear stress present).

  • Fluid Dynamics: Study of fluids in motion (shear stress present).

Fluid Statics

Definition and Properties of Fluids

A fluid is a substance that deforms continuously under the action of shear stress. It does not permanently resist deformation.

• Key Properties of Fluids:

  • Density (ρ): Mass per unit volume of a substance.

  • Specific Gravity (SG): Ratio of the density of a fluid to the density of a reference substance (usually water for liquids).

  • Viscosity: Measure of a fluid's resistance to flow.

  • Surface Tension: The force per unit length existing at the interface between a liquid and another phase.

Classification of Fluids

Compressible vs. Incompressible Fluids

Fluids are classified based on how their density changes with pressure and temperature.

• Incompressible Fluids: Density is not significantly affected by changes in pressure (e.g., most liquids).

• Compressible Fluids: Density varies appreciably with pressure and temperature (e.g., gases).

Key Concept: In a fluid at rest, the pressure at any point is independent of direction (isotropic).

Pressure vs. Force

Definitions and Relationships

Force is the push or pull exerted by a fluid against the walls of its container or on objects within the fluid. Pressure is the force exerted per unit area.

• Pressure (P): , where F is force and A is area.

• Force (F):

  • Where is the gravitational conversion factor (32.174 lbf/lbm-s2 in English units).

  • SI units: F in newtons (N = kg·m/s2), mass in kg, g in m/s2.

  • CGS units: F in dynes.

Hydrostatics of Incompressible Fluids

Hydrostatic Pressure and Head

For an incompressible fluid at rest, the pressure difference between two points is given by:

• Integrating between two points:

• Or, ;

Pressure Head (h): The height of a fluid column that produces a given pressure difference:

Key Point: The pressure at a point in a homogenous, incompressible fluid at rest depends only on the vertical distance below the fluid surface, not on the shape or size of the container.

Hydrostatics of Compressible Fluids

Hydrostatic Pressure in Gases

For compressible fluids (e.g., gases), density varies with pressure and temperature. The hydrostatic equation becomes:

• Integrating (assuming isothermal conditions):

Application: Used to calculate atmospheric pressure changes with altitude.

Manometry: Measurement of Pressure

Manometers and Pressure Measurement

Manometers are devices that measure pressure using columns of liquid. They are commonly used in laboratory and industrial settings.

• Open Manometer: Consists of a vertical tube open to the atmosphere and attached to the container where pressure is measured.

• U-Tube Manometer: A U-shaped tube containing a "gauge fluid" (often mercury or water) to measure pressure differences.

• Differential U-Tube Manometer: Measures the difference in pressure between two containers or points in a system.

• Inclined-Tube Manometer: Used for measuring small pressure differences with higher sensitivity.

General Manometer Equation:

• For a simple U-tube:

• For differential manometers:

Buoyancy and Archimedes' Principle

Buoyant Force and Submerged Objects

When an object is submerged in a fluid, it experiences an upward force called the buoyant force. This force is equal to the weight of the fluid displaced by the object.

• Archimedes' Principle: The magnitude of the buoyant force on an object is equal to the weight of the fluid displaced.

• Buoyant Force (FB):

• Floating Objects: The fraction of the object submerged equals the ratio of the object's density to the fluid's density.

Example: Determining the tension in a cable lowering a block into water, or finding the specific gravity of a body from its weight in air and in water.

Summary Table: Types of Manometers

Key Equations Summary

• Force:

• Pressure:

• Hydrostatic Pressure (Incompressible):

• Hydrostatic Pressure (Compressible):

• Buoyant Force:

Additional info: These notes provide a concise yet comprehensive overview of the fundamental principles of fluid mechanics relevant to chemical engineering and momentum transfer. For detailed problem-solving techniques and further applications, refer to standard fluid mechanics textbooks.