ME 231

FLUID MECHANICS Session 012

Instructor: Dr. Yaling Liu

Syllabus and Homework Instructions

Chapter 1Introduction

Fluids are every where

• Weather, climate (Meteorology)• Rivers, oceans (Environmental)• Flow over aircraft (Aerospace)• Airbag (Mechanical)• Blood flow (Biomedcial)• Others: drinking water

Applications of Fluid Mechanics• Aerospace Vehicle Design

Applications of Fluid Mechanics• Automobile

Applications of Fluid Mechanics• Ship design

Airfoil–flow angle: 14° (2D setting, 3D tetrahedral elements)

Re: 200 – 400, Length: 4 cm, Inflow: 10.3 cm/s, Density: 1 g/cm,

Viscosity: 0.2 - 0.1 g cm / s, Elements: 17181, Nodes: 5840.

Aerospace: Flying Flexible Wing

Movie

Movie

Mechanical: 3D Inflatable Structure

Heart diagram Artificial Heart (AbioCor)

From ABIOMED, Inc.

Biomedical

AbioCor - Principle of Operation

• Mimics native heart• Responds to demand• Few moving parts

AbioCor has two blood pumping chambers•The right side pumps blood into the lungs•the left side pumps the blood into the body

Left VentricleRight Ventricle

Oxygen Poor Blood from Superior/Inferior Vena Cava

Blood out to Pulmonary

Arteries

Oxygen Rich Blood from

Pulmonary Veins

Blood out to Aorta

Left AtriumRight Atrium

Heart model

Dynamics of Large Systems Involving Large Deformation of Heart Muscles and Valves Courtesy of Peskin and McQueen

Left Ventricle

Right Ventricle

Blood In (Source)

Blood In (Source)

Blood Out (Sink)

Approaches in fluid study

• Theoretical (analytical solution, differential equation)

• Numerical (CFD, approximate solution by computers)

• Experimental (measurements, velocity, pressure, etc)

What is fluid mechanics?

• Fluid Mechanics is the science of the mechanics of liquids and gasses

• It is based on the same fundamental principles that are employed in the mechanics of solids.

• Fluid dynamics may be divided into three branches:– Fluid Statics: is the study of the mechanics of fluids at rest;– Fluid Kinematics: deals with velocities and streamlines

without considering forces or energy;– Fluid Dynamics (kinetics): is concerned with the relation

between velocities and accelerations and the forces exerted by or upon fluids in motion.

Introduction 16

What is Fluid?

Definition: It deforms continuously under the application of shear stress.

Solid FluidF

F

t0t1 t2

A. Oztekin © 2005

Characteristics of Fluids

• All matter in nature is found in the form of solid, liquid, or gas and often in a mixture of them - three phases.

• Because of their similarity in dynamic behavior, the two phases, liquid and gas – are designated as FLUIDS.

• Comparing with a solid, a fluid– Does not have a predetermined shape, but rather assume the shape of the

container.– Can not resist externally applied lateral (shear) forces, but instead deforms

continuously under the influence of such forces.– Has “large” molecular spacing relative to a solid and “weak”

intermolecular cohesive force

Introduction A. Oztekin © 2005 18

Basic Equations - Laws

•Conservation of mass

•F = m a

•M = dH / dt ( angular momentum law)

•First law of Thermodynamics

•Second Law of Thermodynamics

•Constitutive Equations: Rigid Body Elastic Solid: = E , = G Ideal Gas: P = R T A. Oztekin © 2005

Continuum Hypothesis

Continuum Hypothesis: Fluids are made of tightly packed particles that occupy a mathematical point with zero dimensions; fluid properties, which are in reality the local average behavior of the molecules around the point, can be thought of as varying continually in space.

Fluids are composed of molecules in constant motion and collision.Microscopic View:

Macroscopic View: Fluids are made of tightly packed particles that interact with each other. Each particle consists of numerous molecules.

P: Fluid particle VP: velocity vector, average molecular velocities

The Continuum assumption allows the use of differential calculus and other related mathematical tools in the analysis of distributed physical systems.

Dimensions and Dimensional Homogeneity

• Dimensions– Qualitatively describe physical qauntities– Basic dimensions: Length (L), Time (T), and Mass (M) – MLT system Length (L), Time (T), and Force (F) – FLT system– All physical quantities can be dimensionally given in terms of the basic

dimensions, i.e. velocity (LT-1), Acceleration (LT-2), Force (MLT-2)– Dimensionless: dimension = 1

• Dimensional homogeneity– All theoretically derived equations are dimensionally homogeneous, e.g.

Introduction 21

symbol variable SI units US customary unitsP pressure Pa ( = 1 N / m2 ) psi ( lb / in2 )

T temperature 0 K ( Kelvin) 0 R ( Rankine)

density kg / m3 slugs / ft3 or lb sec2 / ft4

Primary dimensions in SI system: time, length, temperature, and mass

Primary dimensions in US system: time, length, temperature, and forceSecondary dimensions: velocity, acceleration, volume, flowrate, heat, etc………

Dimensions - Units

A. Oztekin © 2005

Units

• Systems of Units – Quantitatively describe the physical quantities.– International System (SI)

• m (meter), s (second), and kg (kilogram) for length, time, and mass• K (Kelvin) =0C +273.15 for temperature, N=kg m / s2 for force, J = N m for

work (energy or heat), W = J / s = N m/s for power– British Gravitational (BG) System

• ft (feet), s (second), and lb (pond) for length, time, and force• 0R (Rankine) = 0F + 459.67 for temperature, slug = lb s2 / ft for mass, Btu =

778.2 ft lb for work (energy or heat), ft lb/s for power

Introduction A. Oztekin © 2005 23

Example on unitsThe density of mercury is given as 26.3 slugs/ft3.Calculate the specific gravity and specific volume ( in m3/kg ) of mercury.

SG mercury = Hg / H2O(at 4 0 C )

H2O(at 4 0 C ) = 1,000 kg/m3 = 1.94 slug/ft3 (From book tables A.7&8)

SG mercury = 26.3 / 1.94 = 13.56

Introduction 24

Ex. on units cont.1The density of mercury is given as 26.3 slugs/ft3.Calculate the specific gravity and specific volume ( in m3/kg ) of mercury.

kgm107.38

kgm

383.8190.025412

in1m0.0254

ft1in12

kgft

383.8191

kgft

383.8191

kg0.453592lbm1

lbm32.174slug1

slugft

26.31

slugft

26.31

ρ1volumespecific

35

333

33

33

3

A. Oztekin © 2005

Introduction 25

Ex. on units cont.2

The density of mercury is given as 26.3 slugs/ft3. Calculate its specific weight ( in lb / ft3 ) on the moon where g = 5.47 ft / sec2

33

2

23moonmercurymoon

ftlb143.861

ftsec

ftslug5.4726.3

secft5.47

ftslug26.3gργ

A. Oztekin © 2005

Homework

• See calendar