Holly @ 2014 CE

Fundamentals of Fluid Mechanics

Chapter 1: Introduction L1.1 - Characteristics of Fluids

Holly @ 2014 CE

Characteristics of Fluids n  A fluid is defined as a substance that deforms

continuously when acted on by a shearing stress of any magnitude.

n  Fluids: gas, liquid (air, water, syrup?) n  Not-Fluid: Slurries, tar, putty, toothpaste,

(other Bingham plastic materials) n  We assume that molecular spacing is so small

that we can treat the fluid as a continuum) n  (Vacuum: 100 particles/cc; Orion Nebula: E6

particles/cc; Interstellar space: 1 particle/cc)

Dead White (European) Males n  Archimedes, Newton, Bernoulli, Euler, Reynolds, Prandtl,

VonKarman etc n  Rouse & Ince, History of Hydraulics n  Vogle, Life in Moving Fluids n  Calculus: the tool needed to apply laws of mechanics to

fluid behavior (Newton et al)

Holly @ 2014 CE

Holly @ 2014 CE

Analysis of Fluid Behavior Based on Fundamental Laws

of Physics

n  Newton’s laws of motion n  Conservation of mass n  Conservation of momentum n  Conservation of energy n  First and second laws of thermodynamics n  (Will data-mining, neural networks, genetic algorithms

make classical mechanics irrelevant in your lifetime???)

Holly @ 2014 CE

Dimensions

Primary vs Secondary Quantities n  Primary quantities: length (L), time (T), mass

(M), Force (F), temperature (Ө or T) – basic dimensions

n  Secondary physical quantities: area; velocity; density; force; stress; pressure etc. all have basic dimensions

Holly @ 2014 CE

Table 1.1 (p. 5) Dimensions Associated with Common Physical Quantities

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Dimensional Homogeneity n  RULE – Equations expressing laws of

physics must be Dimensionally Homogeneous:

The dimensions (or units) of all terms (i.e. quantities that are combined through addition) MUST be the same maF =

pγ+ z+ u

2

2g=C

Holly @ 2014 CE

Example 1.1

Holly @ 2014 CE

System of Units

Length Time Mass Force Temperature

BG foot (ft)

second (s)

slug (slug)

pound (lb)

Fahrenheit (oF)

EE foot (ft)

second (s)

pound mass (lbm)

pound (lb)

Rankine (oR)

SI meter (m)

second (s)

kilogram (kg)

Newton (N)

Kelvin (oK)

System of Units

Holly @ 2014 CE

Unit Systems

n  British Gravitational (BG) System L-foot (ft), T-second (s), F – pound (lb), M-slug

(slug), T-Fahrenheit (0F) or Ta – Rankine (0R) (F = ma or pound = slug � ft/sec2) q  English Engineering (EE) System L- foot (ft), T- second(s), F – pound (lbf), M-

pound mass (lbm), Ө - Rankine (0R) 1 slug (BG)= 32.174 lbm (EE)

(F = ma or poundforce = poundmass�ft/sec2)

Holly @ 2014 CE

System of Units

n  International System (SI) L-meter (m), T-second (s), F – Newton (N), M-kilogram (kg), θ–Kelvin (K) or Celsius (0C) (F = ma or Newtons = kilograms � m/sec2)

0K=0C+273.15 0F=1.8 x 0C+32

n  What’s the standard gravity in BG, SI, and EE units?

Holly @ 2014 CE

Table 1.3, 1.4 (back cover) Conversion Factors from BG and EE Units to SI Units (You may have to go to other sources for conversions involving e.g. acres, gallons, miles, etc – get the app)

Holly @ 2014 CE

Let unit/dimension checks help you find your errors!

Carry units or dimensions in your equations to ensure dimensional homogeneity Useful to remember: 1 ft = .3048 m; 1 m = 3.2808 ft 1 slug = 14.59 kg; 1 m3 = 1000 litres; g = 9.806 m/sec2 = 32.17 ft/sec2

Work: 1 Joule = 1 newton-meter; 1 BTU = 778.26 ft-lb Power: 1 Watt = 1 joule/sec; 1 HP = 550 ft-lb/sec