Chapter 1

1MEM 320 Fluid Dynamics I

Catalog Description:

Covers equation of motion for compressible flow; static, total, and stagnation concepts; one-dimensional isentropic, normal shock, including Fanno and Rayleigh flows and choked flow; two-dimensional supersonic flow, including Prandtl-Meyer flow and oblique shocks; analysis and design of compressible flow devices, including supersonic nozzles, diffusers, wind tunnels, inlets, and combustors Continuum fluid mechanics

Inviscid (m = 0) Viscous

Compressible Incompressible Compressible Incompressible

Fluid flows can also be classified under regimes :

Laminar ----- motion of laminae or layersTurbulent ----- random three-dimensional motion of fluid particles superimposed on the mean motion

2In MEM 320 we shall primarily focus on Inviscid Compressible Flows (Gas Dynamics)Gas Dynamics(Will this be different from fluid dynamics?)

Gas dynamics is a science in the branch of fluid dynamics concerned with the study of motion of gases and its effects on physical systems

Based on the principles of fluid mechanics and thermodynamics, gas dynamics arises from the studies of gas flows in transonic and supersonic flights.

The studies in gas dynamics are often defined with gases flowing around or within physical objects at speeds comparable to or exceed the speed of sound and causing a significant change in temperature and pressure.

3Chapter 1Fundamentals of Gas Dynamics, 2nd Ed, Zucker and Biblarz

Review of Elementary Concepts

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Expected student background: mathematics (through calculus) + elementary thermodynamics (for stationary systems) elementary fluid mechanics (helpful but not essential)

Chapters 2 and 3 (text): Extension of the laws of thermodynamics in flow systems6

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Using the mass unit of slug (less common):

Using the mass unit of lbm:9

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Density, mass and specific volume do not depend on the value of local gravity.

Weight and specific weight do depend on gravity.

g: the symbol is also used for expressing the ratio of the specific heats at const pressure and constant volume.11

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14ViscosityViscosity is a measure of the resistance of a fluid which is being deformed by either shear stress.

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We shall see very little of viscosity in Chapters 2 8.16

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Thermal equilibrium27

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First Law statements29

Heat and work are path functions (i.e. they are functions of how the system gets from one state point to another)

Hence the symbols

For a stationary (non-flow) system;3031

32Clausius statement:No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature..

Kelvin StatementNo process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.

This means it is impossible to extract energy by heat from a high-temperature energy source and then convert all of the energy into work. At least some of the energy must be passed on to heat a low-temperature energy sink. Thus, a heat engine with 100% efficiency is thermodynamically impossible.

leads to the establishment of a property, viz. entropy

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The second law recognizes the degradation of energy quality by irreversible effectsIrreversible effects: internal fluid friction, heat transfer through a finite temperature difference, pressure non-equilibrium between a system and its surroundingsReversible process: A process in which both the system and its surroundings can be restored to their original state.34

Assuming reversible processNOTE: Equations (1.40) and (1.41) only contain properties (point functions) and are valid for all processes, reversible or not

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For constant specific heats (normally valid over a range of temperatures)37

38g Is also used as specific weight

The property entropy was introduced earlier via Eq. 1.38.39

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Summary of Chapter 1.

Review of basic concepts of thermodynamics and mathematics

What to expect in Chapters 2 and 3

Extension of the laws of thermodynamics in flow systems

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