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Pharos University ME 259 Fluid Mechanics Lecture # 5

Pharos University ME 259 Fluid Mechanics Lecture # 5. Dr. A. Shibl Momentum Equation. Basic Laws. Conservation of mass: dM/dt=0 for system ∂/∂t ∫ ϱ d

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Pharos University ME 259 Fluid Mechanics Lecture # 5

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  1. Pharos UniversityME 259 Fluid Mechanics Lecture # 5 Dr. A. Shibl Momentum Equation

  2. Basic Laws • Conservation of mass: dM/dt=0 for system ∂/∂t ∫ ϱ d𐐏 + ∫ ϱ ⊽. d Ᾱ =0 for control vol. • Newton’s 2nd law Σ F = ma Σ F = ∂/∂t ∫ ⊽ ϱ d𐐏 + ∫ ⊽ ϱ ⊽. d Ᾱ

  3. Momentum Analysis of Flow Systems

  4. Newton’s Laws • Newton’s laws: • First law: a body at rest remains at rest, and a body in motion remains in motion at the same velocity in a straight path when the net force acting on it is zero. • Second law: the acceleration of a body is proportional to the net force acting on it and is inversely proportional to its mass. • Third law: when a body exerts a force on a second body, the second body exerts an equal and opposite force on the first.

  5. Choosing a Control Volume • Fixed, and moving. • For moving CV, use relative velocity,

  6. Body and Surface Forces

  7. Basic Laws for a System • Momentum Equation forInertial Control Volume

  8. Momentum Equation forInertial Control Volume • Basic Law, and Transport Theorem

  9. Linear Momentum Equation • Use RTT to shift from system formulation of the control volume formulation

  10. Momentum Equation forInertial Control Volume

  11. Special Cases • Steady Flow • Average velocities

  12. Basic Laws for a System • The Angular-Momentum Principle

  13. The Angular-Momentum Principle • Basic Law, and Transport Theorem

  14. The Angular-Momentum Principle

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