Download What is Fluids?

Environmental Fluid Dynamics
Instructor: Han Seung Kim
Office: A 1411
TEL: 450-4092
E-mail: [email protected]
Fluid Dynamics and Env. Eng.
What is fluid?
What is the fluid dynamics (mechanics)?
Why is it an important subject in Environmental Engineering?
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Basic media (air, water, groundwater, sludges, organic solvents-NAPLs)
Mass transport (물질전달, macro/micro transport-advection, dispersion, diffusion)
Reaction engineering and reactor/system design (반응공학 및 반응조 설계)
Dimensional analysis (차원해석)
Water management – water resources and quality (수계관리 - 수량, 수질)
Drinking water engineering (상수도공학 - 취수, 도수, 정수, 배수, 관망)
Wastewater engineering (하수도공학 - 배수로, 하수처리장, 배출)
Air quality management (대기관리 - 오염배출, 확산, 배출정화시설, 실내공기정화,
덕트)
Soil and groundwater management (토양, 지하수 관리 및 정화)
What is Fluids?
Phase of materials in nature – Soilds, Liquids, and Gases
“Fluids”
Differences from the solids
 Solids – fixed distances btw. the component molecules → rigid body
(lattice structure) and resistant to shear stress
 Fluids – flexible (varied) mol.-mol. distance and structure → no defined
shape of body and continuously deformed by shear stress, and they can
be equilibrated with shear stress only at motion (운동상태에서만 전단응
력에 대해 평형)
Differences bwt. gases and liquids
 Gases – large and varied mol.-mol. distance, subject to
compression/expansion → varied density (compressible fluids)
 Liquids – relatively constant mol.-mol. distance, almost no
compression/expansion → no density changes (incompressible fluids)
Fluids vs. Solids
Fluids
Solids
Gas or liquid
Solid
A substance can deform
A substance resists a shear
continuously under the action
stress in a static condition
of a shear stress
Irregular or relatively constant
spacing btw. component
molecules
Fixed spacing btw. component
molecules
Free or weakly limited
movement of molecules
Restricted movement of
molecules – lattice structured
Various shapes depending on
containers
Own shapes
Shear stress  time rate of
shear strain
Shear stress  shear strain
Differences btw. Ideal and Non-ideal (real) fluids
 Real – resistance (shear stress) generated in real fluids due to their
viscosity (viscous fluids, 점성 유체)
 Ideal – no viscous effects (inviscid fluid, 비점성 유체), incompressible (비
압축성), useful for the theoretical analysis of fluids
Plastic materials (소성체) – properties of solids and fluids inherent (jellies,
paint, polymeric solutions, paraffin, etc.)
What is “Fluid Mechanics”?
Science that describes physical actions and effects given by the forces
applied to the fluids in motion or no motion.
Classification of Fluid Mechanics

Upon target fluids
1.
2.
3.

Hydrodynamics (동수역학) – incompressible fluids
Gas dynamics (기체동역학) – compressible fluids
Aerodynamics (항공역학) – gases (air) flowing over aircrafts, rockets, etc.
Upon forces applied
1.
2.
3.
Fluid statics (유체정역학) – fluids in no motion, no shear stress but
pressure
Fluid kinematics (유체운동학) – fluid elements in motion
Fluid dynamics (유체동역학) – fluids in motion
Fluids as a Continuum
Fluids composed of individual molecules can be regarded as a hypothetical
homogenous continuum (hypothetically continuous substance) for their
mathematical analysis.
A way of describing the behavior of fluid in a given field of flow by considering the
average effects of the molecules in a given volume.
The number of molecules in the air at 1 atm and 0oC = ~ 107/mm3
 Fluid element: Very small pieces of fluids that posses the characteristics of fluids,
Not fluid molecules
Rationale (e.g., gases)
 Very short mol.-mol. distance (molecular mean free path ~ 10-5cm)
 Time scale for the mol.-mol. collisions << one for the system on which fluids work
(e.g., forces)
force
force
time
time
Mass, force, weight
Mass - a property of physical objects that measures the amount of
matter they contain, the property of a body that causes it to have
weight in a gravitational field. Constant anywhere in space. (g, kg,
slug, lbm)
Force – a physical property that gives the movement of a static
object or changes in velocity or direction of an object in motion (F
= ma, N, kgf, dyne, lbf)
Weight - the vertical force exerted by a mass as a result of gravity (W
= mg)
Class quiz
A substance of which mass is 10kg weighs 8.9kgf on a planet. What is the
acceleration of gravity on this planet? (질량이 10kg인 물체를 저울로 달
았더니 8.9kgf이었다. 이곳의 중력가속도는?)
A substance weighs 100kgf on the earth. What are the mass and weight of
this substance on a planet of which acceleration of gravity is 1/5 of that
of the earth? (지구상에서 100kgf인 물체를 중력가속도가 지구의 1/5인 위
성으로 가져가면 질량과 중량은 각각 얼마인가?)
What is the weight of a pound mass (lbm) on the earth’s surface, where the
acceleration due to gravity is 32.2 ft/s2, and on the moon’s surface,
where the acceleration is 5.31 ft/s2?
Basic fluid properties
Mass density (중량밀도, 밀도,  ) = m/vol. kg/m3, lbm(or slug)/ft3
Specific weight (단위중량, 비중량, g ) = W/vol. =  g, N/m3, lbf/ft3
Specific volume (단위체적, 비체적, Vs) = 1/ , 1/ g (in weight unit, 중력단위계)
Specific gravity (비중, S, dimensionless) =
for liquids,
 fluid  fluid

 water  water
for gases,
 gas  gas M .W .gas


 air  air M .W .air
where, water (or water):  (or ) of water at 4oC
and air (or air):  (or ) of air at 1atm and 0oC.
Ideal gas law
pV = nRuT where, Ru: universal gas constant (8.31 kJ/kmol-oK, 1545 ft-lbf/lbmol-oR)
→ In fluid mechanics, p= RT where, R: gas constant ( ~J/kg-K, ft-lbf/slug-oR)
Density (mass) of gas,  
p
RT
Class quiz)
Density of air at standard sea-level pressure (atmospheric pressure)
and 0, 4, and 20oC?
Specific gravity and density of Helium at 1 atm, 0oC?
Specific gravity of mercury?
What are the specific weight, specific volume, and density of carbon dioxide gas (CO 2)
at 101.3 Kpa and 100oC?
Specific heat (비열, c): , kJ/kg-oC
정적비열 (cv), 정압비열(cp), 비열비 (specific heat ratio, k) = cp / cv
Specific internal energy (비내부 에너지, u): J/kg
= f(temp., pressure) for real gas
= f(temp.) for ideal gas
Elasticity (탄성) – compressibility (압축성)
Bulk modulus of elasticity (체적탄성계수, Ev) ~N/m2
= -dP/(dV/V) = dP/(d/)
Class quiz) A liquid has a volume of 0.4m3 and 0.396m3 in a container
pressurized at 1000kgf/cm2 and 2000kgf/cm2, respectively. What is the
bulk modulus of elasticity (Ev) of this liquid?
Viscosity (점성)
Fluids in motion tend to internally resist to the relative motion generated between fluid
layers when external shear stress is applied. This property is called “viscosity”.
Newton’s law → shear stress btw. fluid layers ()  relative deformation btw. fluid
layers (dV/dy, shear rate)
dV
 
dy
: dynamic/absolute viscosity (동역학적/절대 점성계수)
 (= /): kinematic viscosity (동점성계수)
Viscosity of gases vs. liquids
Driving forces for viscosity – molecular cohesive force (분자응집력), molecular momentum
exchange (분자 운동량 교환)
In gasses – primarily controlled by molecular momentum exchange – viscosity  with temperature
In liquids – by molecular cohesive force – viscosity  with temperature
For gases – Sutherland equation
3
2
  T  T0  S
  
0  T0  T  S
where, 0: dynamic viscosity at T0 S: Sutherland
constant (see Table A.2)
For liquids
 = Ceb/T
Where, C, b: empirical constants
Class quiz)
A board (1m 1m, 25N weight) slides down an inclined ramp (slope=20o) with a
velocity of 2 cm/s. The board is separated from the ramp by a thin film of oil with a
viscosity of 0.05Ns/m2. Calculate the spacing between the board and ramp.
(Neglect edge effects)
Newtonian vs. Non-Newtonian fluids
Newtonian fluids – shear stress is linearly related to shear rate (water, air, lowmolecular liquid)
Non-Newtonian fluids - shear stress is NOT linearly related to shear rate
Bingham – ketchup, toothpaste
Shear-thinning (psedoplastic) – polymeric
solution, slurries, sludge, pulp solution
Shear-thickening (dilatent) – resin, highly
heated glass, asphalt
Surface tension
When a liquid is in contact with different phases (e.g., gas, solids), liquid molecules at
the surface exert “tension” on adjacent surface due to their greater attraction btw.
the molecules at the surface than those below the surface (cohesive force, 응집
력 > adhesive force, 부착력). → interfacial tension (surface tension,  : liquid-gas
contact)
Defined as “tension force per unit length”, ( ) –  of water at room temp.= 0.073 N/m
  1/temp
The surface tension is typically ignored in most cases, but it must be taken into
account in very small scale flow (gas/liquid droplets present, small scale models,
etc.)
How to measure? – capillary rise technique, ring tensiometer (Du Nouy ring method),
contact angle measurement method
Capillary rise technique
Capillary tube (d < 1 cm)
Typically, =0o for water and clean glass
Vertical component of the surface tension,
F,z = d cos
Weight of water risen
W = (h)(d2/4)
At equilibrium, F,z = W
h = 4 cos / d
Contact angle ()
determines wetting/non-wetting phases
~ f (cohesive, adhesive forces)
<90o
air
>90o
air
mercury
water
glass
adhesive btw. liquid/solid > cohesive btw. liquid molecules
glass
adhesive btw. liquid/solid < cohesive btw. liquid molecules
Examples of surface tension
Wt  2F  2L
F  L  pA
F  L  pA
2r  pr 2
2r  2  pr 2
2
p
r
p
F  F ,inside  F ,outside
  ( Dinside  Doutside)
4
r
Vapor pressure (Pv, 증기압)
The pressure at which a liquid boils
Pv  temp
Ex) water boils at 100oC (212oF) and 1 atm (14.7 psia) and also
boils at 10oC (50oF) and 0.178 psia.
Important for cavitation (공동현상)
Fluid statics (유체정역학)
Deals with the fluids in no motion.
Forces applied on the fluids
1. Surface forces (표면력) – Pressure in vertical direction, viscous shear stress in
tangential direction
2. Body forces (체적력) – External forces with no contact (e.g., gravity), = f(mass
and volume of fluids)
→ In fluid statics, just consider pressure and gravity (no shear stress!)
Pressure? – dF/dA
Gravity? – W=V
Pressure at a point in a static fluid acts
with the same magnitude in all directions.
Pn=Px=Py=Pz
Pascal’ law
A pressure change produced at one point in a closed system is transmitted
throughout the entire system. (p1 = p2 = p3 = …. = pn)
예제 3.1) If a force of 100N were
exerted on the handle of this hydraulic
jack, what load, F2, can the jack
support? Neglect lifter weight.
Abs. vs. Gage pressure (절대, 계기 압력)
“0” pressure (vacuum) is the absolute pressure.
→ atmospheric pressure at sea level = 101.3 kN/m2 (kPa abs.), 14.6 psia.
Gage pressure = abs. pressure + atmospheric pressure
Negative gage pressure → vacuum pressure
Pressure variation with elevation
dp
 
dz
Pressures are constant along a horizontal path, but vary along a vertical path
(gravity direction).
If no density change ( constant-incompressibie fluids),
P + z = const. (piezometric pressure)
P/ + z = const. (piezometric head)
Class quiz)
Ex 3.3)
Ex 3.4)
Compressible fluids (기체)
Assumption – ideal gas
 = p/RT,  = pg/RT
→Pressure variation = f (z, temp)
dp
pg
   
dz
RT
In troposphere (대류권)
temp  with elevation
T = T0 - (z-z0)
 T   ( z  z0 ) 
p  p0  0

T0


g
R
In stratosphere (성층권)
constant temp with elevation
p  p0e
( z  z0 )
g
R
Pressure measurement
Pressure gage
1. Manometer (액주계)
Bourden-tube gage
Pressure measurement
Differential manometer (시차액주계)
p2  p1    i hi   i hi
down
up
p( p1  p2 )  ( m   f )h
Class quiz)
A differential mercury manometer is connected to two pressure taps in an
inclined pipe as shown. Water at 50oF is flowing through the pipe. The
deflection of mercury in the manometer is 1 inch. Find the difference in
piezometric pressure and piezometric head btw. the two points.
Hydrostatic forces (정수력)
Forces given by the hydrostatic pressure (정수압, 정압) applied on a
submerged plate in a no-motion fluid
Note)
The first moment of area (단면 1차 모멘트) =
 ydA  y A
A
The second moment of area (단면 2차 모멘트)=
2
 y dA  I  y A
2
A
How much is the magnitude of hydrostatic force?
Fhydrostatic  p A
Where does the hydrostatic force act on a submerged plate?
ycp  y 
I
yA
Class quiz)
The end of pipe is closed by an elliptical
shape gate (54 m) and the gate is
fixed by a hinge at its top. How much
of normal force is required to open
the gate? Neglect the weight of the
gate.
Class quiz)
Find the magnitude of the hydrostatic force acting on one side of the
submerged vertical plate given below and also find the location of the
center of pressure.
Hydrostatic forces on curved surfaces
Integrating pressure force along the curved surface
Easier way – use free-body diagram (자유물체도) and consider force equilibrium
in vertical/horizontal directions
Fh  FAC
Fv  FBC  W
F  Fh  Fv
2
  tan 1
Fv
Fh
2
Class quiz)
Find the magnitude and line of action of
the hydrostatic force acting on
surface AB (the thickness of the
circular AB is 1 m).
Buoyant force (부력)
A resultant hydrostatic force that acts on the surfaces of a body submerged or
floating in fluids
Net vertical forces acting on a body a body submerged or floating in fluids
1) Submerged body
FB = Fup - Fdown = (Vb+ Va) - Va = Vb = VD
where, Va: vol. ABCEF,
Vb: vol. of the body,
VD: displaced volume (배수체적)
2) Floating body
0
FB = Fup - Fdown = VD (Fdown = Patoms. A = 0)
Archimedes’ principle
1. A body submerged in a fluid receives a
buoyant force as much as the weight of
the displaced volume of the fluid.
2. A body floating in a fluid displaces a
volume of the fluid corresponding to the
weight of the submerged part of the body.
Apparent weight (겉보기 무게) of a body in a fluid
From the equilibrium of forces,
T
T + FB = W
Apparent weight, T = W – FB
W
FB
 ( body   fluid )Vbody
Hydrometer (비중계)
Density of a fluid of interest → buoyancy
difference → Difference in hydrometer
submerging (측정하고자 하는 유체의 밀
도 → 부력차 → 가라앉는 정도의 차이)
 Specific weight (단위 중량), specific
gravity (비중)
Class quiz)

What are the volume and specific gravity of a body that weighs 60N and 11N
in the air and water, respectively? (Neglect the mass of air)?

A floating iceberg exposes 10% of its body (by volume) above the surface of
sea water of which specific gravity is 1.03. What is the specific gravity of this
iceberg?

A hydrometer of which weight is 20g and diameter is 6mm submerges in a
fluid by 6 cm more than when it has been used for water. Find the specific
gravity of this fluid.
Class quiz)
The woodblock (505010 mm) has a specific gravity S1 = 0.3 and the volume
of the metal part is 6600 mm3. Mass of the metal part and the tension T of
the cord?
Free-body diagram