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Fluid Flow Concepts and Basic

Control Volume Equations

Introduction

Control Volume Conservation Equation

Conservation of Mass/Continuity

CE 2200

Fall 2015

Chapter 5

Dot Product

u v u v• = cos

θ

q!

u

v

normal unit vector, n

• magnitude of one

• direction is normal to the surface

Area vector, A = nA

Differential Area vector, dA = ndA n

A

Surface

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CE 2200/Willson February 27, 2015 2

Flow Rate

dA

V

∫

∑•=Δ•=

area

area

AdvAvQ

Q v dA

area

=∫cos

θ

Q v A= •

dA

V

Flow Rate

Mean, or average velocity

turbulent flow: the mean velocity may closely approximate

the actual flow

laminar flow: the mean velocity probably doesn’t approximate

the actual flow

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CE 2200/Willson February 27, 2015 3

Control Volume Approach

System: a given quantity of matter

For solids---use system approach with Lagrangian viewpoint

For fluids---this approach is too complicated for most systems

Control Volume Approach

mass momentum energy

Extensive Property, B

Intensive Property, β = B/m

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