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Section
5: Control Volume Theorums |
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5.1 |
Physical
laws expressed first in terms of a material particle and then in terms of
a material volume - a closed system that consists always of the same material
particles: law of mass conservation, equation of motion, first law of thermodynamics,
second law of thermodynamics. |
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5.2 |
The
Reynolds transformation, which allows the physical laws that apply to material
volumes to be re-expressed so they apply to an arbitrarily specified control
volume æan open system with a completely arbitrarily specified boundary. |
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5.3 |
The
mass conservation law applied to a control volume. Examples involving various
control volume choices for a given problem. |
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5.4 |
The
linear momentum equation (Newton's law of motion in control volume form).
Various examples, steady and unsteady, including a fuel-laden space rocket
accelerating to speed, transient flows involving phase change (and the reaction
stress that causes), examples from hydraulics and surface waves, determining
drag from a wake profiles, etc. |
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5.5 |
The
angular momentum theorem (a moment of Newton's law, expressed in control
volume form). Various examples, ranging from lawn sprinklers and centrifugal
pumps to the transient spin-up of bathtub vortices and tornadoes. |
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5.6 |
The energy
equation (first law of thermodynamics) and the second law of thermodynamics
in control volume form. |
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Reading
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Fay, Chapter 5
A. A. Sonin, "Fundamental Laws of Motion For Particles,
Material Volumes and Control Volumes", 2001 [PDF]
and "On Choosing and Using Control Volumes: A Simple Example"
[PDF]
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| Problem
Set Section - 5 |
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| Problem
5.1: Force on Nozzle |
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| Problem
5.2: Fireman's Hose |
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| Problem
5.3: Sluice Gate |
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| Problem
5.4: Hydraulic Jump |
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| Problem
5.5: Sudden expansion |
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| Problem
5.6: Narrowing stream from tap |
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| Problem
5.7: Pressure drop in reaction |
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| Problem
5.8: Jet pump |
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| Problem
5.9: Scrubber |
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| Problem
5.10: Nozzle - in and out flows |
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| Problem
5.11: Air cushion vehicle |
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| Problem
5.12: Hovering platform |
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| Problem
5.13: Rain on roof |
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| Problem
5.14: Sand onto rolling plate |
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| Problem
5.15: Hinged flat plate |
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| Problem
5.16: Rocket assisted braking |
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| Problem
5.17: Rocket accelerating |
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| Problem
5.18: Rocket on test bed |
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| Problem
5.19: Spherical combustion |
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| Problem
5.20: Solid disc spinning up |
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| Problem
5.21: Radial outflow spinning |
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| Problem
5.22: Torque on S-bend |
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| Problem
5.23: 2D split jet |
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| Problem
5.24: Mass flow from torque |
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| Problem
5.26: Lawn sprinkler |
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| Problem
5.27: Centrifugal pump-turbined |
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| Problem
5.28: Steady sink flow |
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| Problem
5.29: Startup of circulation |
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