







Section
5: Control Volume Theorums 



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. 

5.2 
The
Reynolds transformation, which allows the physical laws that apply to material
volumes to be reexpressed so they apply to an arbitrarily specified control
volume æan open system with a completely arbitrarily specified boundary. 

5.3 
The
mass conservation law applied to a control volume. Examples involving various
control volume choices for a given problem. 

5.4 
The
linear momentum equation (Newton's law of motion in control volume form).
Various examples, steady and unsteady, including a fuelladen 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. 

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 spinup of bathtub vortices and tornadoes. 

5.6 
The energy
equation (first law of thermodynamics) and the second law of thermodynamics
in control volume form. 


Reading


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]


Problem
Set Section  5 



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 Sbend 
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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 pumpturbined 
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Problem
5.28: Steady sink flow 
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Problem
5.29: Startup of circulation 
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