pharos university me 259 fluid mechanics lecture # 5 dr. a. shibl momentum equation
TRANSCRIPT
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Pharos UniversityME 259 Fluid Mechanics
Lecture # 5
Dr. A. Shibl Momentum Equation
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Basic Laws • Conservation of mass: dM/dt=0
for system∂/∂t ∫ ϱ d 𐐏 + ∫ ϱ ⊽. d Ᾱ =0 for
control vol.
• Newton’s 2nd law Σ F = ma Σ F = ∂/∂t ∫ ⊽ ϱ d 𐐏 + ∫ ⊽ ϱ ⊽. d Ᾱ
Apr 21, 2023 2/27
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Momentum Analysis of Flow Systems
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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.
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Choosing a Control Volume• Fixed, and moving.
– For moving CV, use relative velocity,
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Body and Surface Forces
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Basic Laws for a System
• Momentum Equation forInertial Control Volume
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Momentum Equation forInertial Control Volume
• Basic Law, and Transport Theorem
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Linear Momentum Equation
• Use RTT to shift from system formulation of the control volume formulation
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Momentum Equation forInertial Control Volume
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Special Cases
• Steady Flow
• Average velocities
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Basic Laws for a System
• The Angular-Momentum Principle
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The Angular-Momentum Principle
• Basic Law, and Transport Theorem
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The Angular-Momentum Principle
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