(1)introduction
TRANSCRIPT
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