Pharos UniversityME 259 Fluid Mechanics

Lecture # 5

Dr. A. Shibl Momentum Equation

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 19, 2023 2/27

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 forInertial Control Volume

Momentum Equation forInertial Control Volume

• Basic Law, and Transport Theorem

Linear Momentum Equation

• Use RTT to shift from system formulation of the control volume formulation

Momentum Equation forInertial 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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