Download Pharos University Fluid Mechanics For Electrical Students

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 d𐐏 + ∫ ϱ ⊽. d Ᾱ =0 for control
vol.
• Newton’s 2nd law Σ F = ma
Σ F = ∂/∂t ∫ ⊽ ϱ d𐐏 + ∫ ⊽ ϱ ⊽. d Ᾱ
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Momentum Analysis of Flow
Systems
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.
Choosing a Control Volume
• Fixed, and moving.
– For moving CV, use
relative velocity,
Body and Surface Forces
Basic Laws for a System
• Momentum Equation for
Inertial Control Volume
Momentum Equation for
Inertial Control Volume
• Basic Law, and Transport Theorem
Linear Momentum Equation
• Use RTT to shift from system formulation of the
control volume formulation
Momentum Equation for
Inertial Control Volume
Special Cases
• Steady Flow
• Average velocities
Basic Laws for a System
• The Angular-Momentum Principle
The Angular-Momentum Principle
• Basic Law, and Transport Theorem
The Angular-Momentum Principle
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