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Fluid Mechanics-61341

An-Najah National UniversityCollege of Engineering

Chapter [6]

Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle Dr. Sameer Shadeed1

Dr. Sameer Shadeed

Chapter [6]

Momentum Principle

Momentum

MomentumMomentum = Mass X Velocity

Momentum Momentum can be linear or angular

Linear:Linear: deals with issues such as collisionsLinear:Linear: deals with issues such as collisions

Angular:Angular: due to rotation of planet

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Linear Momentum

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Newton’s 2nd Law2nd Law:

Definition of linear momentumlinear momentum:

or

Linear Momentum

Conservation of momentummomentum:

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Conservation of Momentum

The conservationconservation ofof linearlinear momentummomentum principleprincipletells us: If a system is isolated, its total linearmomentum does not change

Particles move about in a box: No particles leave orenter, hence the box is a system

Particles can exchange momentum with each other, but that does not affect the total momentum of the system

The only way to change the total momentum is to apply a force to the box

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Therefore:

Conservation of Momentum

Notice the similarities and differences betweenconservation of mass and momentum:

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(conservation of mass)

(conservation of momentum)

Both equations are applied to the system MassMass is conserved absolutely; MomentumMomentum is conserved

unless a force is applied

Momentum Equation

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Momentum Equation

To summarize, we can say , in general in general , that

Rate of change ofmomentum in the givendirection of the fluid passingthrough the control volume

Total force exertedon the fluid in acontrol volume ina given direction

=

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through the control volumea given direction=

Pipe Flow Application

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Pipe Flow Application

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Pipe Flow Application

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Pipe Flow Application

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Example 1

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Example 1 (Solution)

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Example 1 (Solution)

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Example 1 (Solution)

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Example 1 (Solution)

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Example 1 (Solution)

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Pipe Flow Application

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Pipe Flow Application

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Pipe Flow Application

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Example 2

Upstream from an axisymmetric abrupt enlargement ina horizontal passage the mean pressure is 140 kPa andthe diameter is 150 mm. Downstream from theenlargement the mean pressure is 210 kPa and thediameter is 300 mm. Estimate the flowrate through thepassage and the force on the enlargement

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passage and the force on the enlargement

Example 2 (Solution)

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Example 2 (Solution)

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Open Channel Flow Application

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Open Channel Flow Application

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Open Channel Flow Application

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Example 3

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Example 3 (Solution)

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Example 3 (Solution)

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Open Channel Flow Application

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Open Channel Flow Application

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Open Channel Flow Application

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Example 4

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Example 4 (Solution)

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Example 4 (Solution)

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Example 4 (Solution)

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