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Lectures-14 & 15: Chapter 6

Momentum Equation

Objectives: Use control volume analysis to

determine forces associated with fluid flow.

Outline

Derivation of Momentum Equation

Interpretation of the Momentum Equation

Procedures for Using Momentum Equation

Examples

Navier-Stokes Equations

Summary

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6-1: Linear Momentum

Equation: Derivation

Reynolds transport theorem (by setting B = ___ and b = __)

Linear momentum equation

Here Vr= _______is the fluid velocity relative to the control

surface (for use in mass flow rate calculations at all locations

where the fluid crosses the CS), and Vis the fluid velocity as

viewed from an inertial reference frame. The product

(Vr.n)dA represents the mass flow rate through area

element dA into or out of the CV.

CSCV dnd

tdt

dAVVV

Mom

r

sys

(1a) dAnVVdV

t

FCV CS r

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Linear Momentum Equation:

Derivation: Special Cases

For a fixed control volume (no motion or deformation of

control volume), Vr= _and the linear momentum equation

becomes

Note that the momentum equation is ______ equation, and

thus each term should be treated as a vector.

For steady flow

Most momentum problems considered in this text are

steady.

(1b) :CV Fixed dAnVVdV

t

FCV CS

(1c) dAnVVF CS r

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