Intoduction Chee 223 1.1

Introduction to Fluid Mechanics

• Fluid Mechanics is concerned with the behavior of fluids at rest and in

motion

• Distinction between solids and fluids:

– According to our experience: A solid is “hard” and not easily

deformed. A fluid is “soft” and deforms easily.

– Fluid is a substance that alters its shape in response to any force

however small, that tends to flow or to conform to the outline of its

container, and that includes gases and liquids and mixtures of solids

and liquids capable of flow.

– A fluid is defined as a substance that deforms continuously when

acted on by a shearing stress of any magnitude.

Intoduction Chee 223 1.2

Course Organization

Textbook: deNevers “Fluid Mechanics for Chemical Engineers”

Introduction (Chapter 1) / Dimensions, Units

Fluid statics: Fluid is at restFluid mechanics

Fluid dynamics: Fluid is moving

Fluid statics (Chapter 2): Pressure, measurement of pressure, hydrostatic forces, buoyancy

Fluid dynamics (Chapters 3-5, 7): Mass, energy and momentum balances Applications in Engineering (Chapters 6, 9, 11, 12): Flow in pipes,

turbomachines, flow over immersed bodies, flow through porous media Dimensional analysis and modeling (Chapter 13)

Intoduction Chee 223 1.3

Introduction

Intoduction Chee 223 1.4

Dimensions and UnitsIn fluid mechanics we must describe various fluid characteristics in terms of certain basic quantities such as length, time and mass

• A dimension is the measure by which a physical variable is expressed qualitatively, i.e. length is a dimension associated with distance, width, height, displacement.

Basic dimensions: Length, L (or primary quantities) Time, T

Mass, MTemperature,

We can derive any secondary quantity from the primary quantities i.e. Force = (mass) x (acceleration) : F = M L T-2

• A unit is a particular way of attaching a number to the qualitative dimension: Systems of units can vary from country to country, but dimensions do not

Intoduction Chee 223 1.5

Dimensions and Units

Primary Dimension

SI UnitBritish

Gravitational (BG) Unit

English Engineering (EE) Unit

Mass [M] Kilogram (kg) SlugPound-mass (lbm)

Length [L] Meter (m) Foot (ft) Foot (ft)

Time [T] Second (s) Second (s) Second (s)

Temperature [] Kelvin (K) Rankine (°R) Rankine (°R)

Force [F]Newton

(1N=1 kg.m/s2)Pound (lb) Pound-force (lbf)

Conversion factors are available in the textbook inside of front cover.

Intoduction Chee 223 1.6

Units of Force: Newton’s Law F=m.g

• SI system: Base dimensions are Length, Time, Mass, Temperature

A Newton is the force which when applied to a mass of 1 kg produces an acceleration of 1 m/s2.

Newton is a derived unit: 1N = (1Kg).(1m/s2)

• BG system: Base dimensions are Length, Force, Time, Temperature

A slug is the mass which produces an acceleration of 1 ft/s2 when a force of 1lb is applied on it:

Slug is a derived unit: 1slug=(1lb) (s2)/(ft)

• EE system: Base dimensions are Length, Time, Mass, Force and Temperature

The pound-force (lbf) is defined as the force which accelerates

1pound-mass (lbm), 32.174 ft/s2.

Intoduction Chee 223 1.7

Units of Force – EE system

To make Newton’s law dimensionally consistent we must include a dimensional proportionality constant:

cg

gmF

where

2f

mc )s)(lb(

)ft)(lb(1740.32g

Intoduction Chee 223 1.8

Example: Newton’s Law

• An astronaut weighs 730N in Houston, TX, where the local acceleration of gravity is g=9.792 m/s2. What is the mass of the astronaut? What is his weight on the moon, where g=1.67 m/s2?

• Redo the same problem in EE units. In EE units the astronaut weighs

164.1lbf, gHouston=32.13 ft/s2 and gmoon=5.48 ft/s2.

Intoduction Chee 223 1.9

Dimensional Homogeneity

• All theoretically derived equations are dimensionally homogeneous:

dimensions of the left side of the equation must be the same as those

on the right side.

– Some empirical formulas used in engineering practice are not

dimensionally homogeneous

• All equations must use consistent units: each term must have the

same units. Answers will be incorrect if the units in the equation are

not consistent. Always chose the system of units prior to solving the

problem

Intoduction Chee 223 1.10

Properties of Fluids

Fundamental approach: Study the behavior of individual molecules

when trying to describe the behavior of fluids

Engineering approach: Characterization of the behavior by considering

the average, or macroscopic, value of the quantity of interest, where the

average is evaluated over a small volume containing a large number of

molecules

Treat the fluid as a CONTINUUM: Assume that all the fluid

characteristics vary continuously throughout the fluid

Intoduction Chee 223 1.11

Measures of Fluid Mass and Weight• Density of a fluid, (rho), is the amount of mass per unit volume of a

substance: = m / V

– For liquids, weak function of temperature and pressure

– For gases: strong function of T and P

from ideal gas law: = P MR T

where R = universal gas constant, M=mol. weight

R= 8.314 J/(g-mole K)=0.08314 (liter bar)/(g-mole K)=

0.08206 (liter atm)/(g-mole K)=1.987 (cal)/(g-mole K)=

10.73 (psia ft3)/(lb-mole °R)=0.7302 (atm ft3)/(lb-mole °R)

)T,P(

(1.1)

Intoduction Chee 223 1.12

Measures of Fluid Mass and Weight

• Specific volume: = 1 /

• Specific weight is the amount of weight per unit volume of a substance:

= w / V = g

• Specific Gravity (independent of system of units)

C4@OH2

SG