Upload
liz-bargola
View
728
Download
1
Tags:
Embed Size (px)
DESCRIPTION
Review Handout from Dr. Olano
Citation preview
FLUID MECHANICS
Manila Review Institute Chemical Engineering Review
Dr. Servillano Olano, Jr
Fluid Mechanics
� Fluid mechanics
� Branch of engineering science that has to do with the behavior of fluids (liquids, gases and vapors)
� Branches of Fluid Mechanics
1. Fluid Statics
� Fluids in equilibrium state of no shear stress
2. Fluid Dynamics
� Portions of the fluid are in motion relative to
the other parts
Fluid Statics
Nature of Fluids
A fluid is a substance that does not
permanently resist distortion.
Some physical properties of fluids:
a) Density or relative density
b) Viscosity
c) Surface tension
� Types of Fluids
1. Incompressible
� Density is not affected by changes in temperature and pressure
2. Compressible
� Density varies appreciably with temperature and pressure
� Pressure Concept
� For a static fluid, the pressure at any point is independent of direction.
Fluid Mechanics
English SI
Length, L ft., inch meter (m)
Mass, M lbm, slugs Kg
Time, T seconds (s), hr s
Force, F lbf newton (N)
Density, ρ lbm/ft3, slug/ft3 Kg/m3
Systems of Units
Relationship between Force and Mass: F=ma
2
2
32.16ENGLISH:
32.16c
ftg lbfsF m lbm lbm lbf
lbm ftg lbm
lbf s
= = =⋅⋅
2 2SI: 9.806 ( )m mF mg kg kg newton Ns s
= ⋅ = ⋅ =
Fluid Statics and Applications
Hydrostatic Equilibrium
Force balance:
- ( ) - 0
0
c
c
gp S p dp S Sdz
g
gdp dz
g
ρ
ρ
+ =
+ =
Fluid Statics and Applications
2 11 2
constant
( )
c
c
p gz
g
p p gz z
g
ρ
ρ ρ
+ =
− = −
Hydrostatic Equilibrium,
for constant density (most liquids)
0
0
c
c
pM gdp dz
RT g
dp gMdz
p g RT
+ =
+ =
Barometric EquationFor an ideal gas, ρ = (pM/RT).
Substituting,
Fluid Statics and Applications
Integrating between levels 1 and 2:
( )
( )
22 1
1
2 12
1
ln
exp
c
c
p gMz z
p g R T
gM z zp
p g R T
= − −
− = −
(Called the barometric equation)
Fluid Statics and Applications
2. Simple Manometers
Pressure balance at level 0:
ρρρ
ρρρρρ
zg
gH
g
gpp
g
gH
g
ga
g
gzp
g
ga
g
gHp
c
mm
c
c
mm
cccc
m
∆+−=−
++∆+=++
)(21
21
Simplifying gives:
Fluid Statics and Applications
Two-fluid U-tube Manometer
Pressure balance at point 0:
=∴
=
−+−=−
++=++
A
aHh
hAaHbut
ghgHpp
gHhpgHhp
m
m
ABBmm
mmBBmA
)()(
)()(
21
21
ρρρρ
ρρρρ
Viscous forces in a fluid
Rheological Properties of Fluids
Evaluation of Fanning friction factor
Fluid Dynamics and Applications
Evaluation of surface roughness factor
Flow of Incompressible Fluids
3. Turbulent flow in pipes and closed channels
(correlation equations)
(Values of α and β are close to unity)
(((( ))))
(((( )))) 400041
6000641
8
51
915
81
2
2
.fNlog.f
.fNlog.f
fk
fkk
f
Re
Re
−−−−====
−−−−====
++++====
−−−−++++====
ββββ
ααααk = 0.40
Von Karman eq
Nikuradze eq.
Flow of Incompressible Fluids
Other Correlations for f:
Blassius Formula: (for smooth tubes)
Colebrook Equation:
Churchill Equation:
Evaluation of Ff (for fittings and valves)
Entrance section of a pipe
� For fully developed velocity profile:
For laminar flow:
For turbulent flow:
Ree N.
D
L05750====
50≅≅≅≅D
Le
Le
Coverage Chart
Classification of Pumps
Examples of Pumps
A. Centrifugal pumps
Dynamic pumps
B. Reciprocal pumps
Positive displacement pumps
C. Gear pumps
D. Axial flow pumps
Simple Centrifugal Pump
Examples of Pumps
Examples of Pumps
Examples of Pumps
Characteristic Curves
Characteristic Curves of Centrifugal Pumps
Guide in the selection of Pumps
System head vs Available head
Net Positive Suction Head (NPSH)
� Head available at the pump inlet to keep the liquid from cavitating or boiling
Where: ps = pressure at suction point
pv = vapor pressure of the liquid
If NPSH <= 0, cavitation will occur
Note: NPSH(available) should be greater than NPSH(required)
ρρ
ρρ
v
c
s
c
a
vsa
pF
g
v
g
gz
pNPSH
ppNPSH
−∑−−+=
−=
)2
(
2
11
Flow Meters
a) U-Tube Manometer
p1 – p2 = Hm (ρm - ρ)
or
where: Hm = manometer reading
∆H = differential head
ρm = density of manometer liquid
−−−−
ρρρρ
ρρρρ====
ρρρρ
−−−−====∆∆∆∆ 1H
ppH m
m21
Pitot Tube
If tube opening is placed at the center,
(for incompressible fluids)
where
vcpmax Hg2Cv ∆∆∆∆====
−−−−
ρρρρ
ρρρρ====∆∆∆∆ 1HH m
mv
Flow Metersa) Pitot Tube (measurement of local velocity)
By MEB Eq:
ρρρρ
−−−−==== c12
p
g)pp(2Cv
Pitot TubeTo get average velocity, vav:
Where
see Fig. 2.10-2 G, to get vav
For gases at velocities > 200 fps, see Eq. 10-8, Perry.
(((( ))))maxRe,Re
max
av NorNfv
v====
µµµµ
ρρρρ==== max
maxRe,
DvN
Flow Metersc) Head Meters (Orifices, venturi meters,
nozzles)
Head MetersEvaluation of Y: f (type of fluid)
�For liquids, Y = 1.0
�For gases, see Fig. 10-16, Perry
Evaluation of C (discharge coefficient)
Types of Taps:
Rotameters (or Area Meters)
� Force Balance:
where
� vf = velocity of float
� ρf = density of float
� Af = max. cross-sectional area of float
)p(Ag
g)(v f
c
ff ∆∆∆∆−−−−====ρρρρ−−−−ρρρρ
cf
ff
gA
g)(vp
ρρρρ−−−−ρρρρ====∆∆∆∆
Rotameters
� In most cases, the geometry of the rotameter is not known, so a calibration curve using water is prepared. To determine flowrates for other liquids or gases, the above relation is used.
� In terms of velocity
� For an identical flowmeter
(a linear relationship)
f
ffoR111
A
v)(g2ACAv
ρρρρ−−−−ρρρρρρρρ====ρρρρ
o
'
R1 ACv ≈≈≈≈
Rotameters (or Area Meters)
� Substituting in the General Equation:
� Since 1 - β4 ≅ 1.0
� For values of CR, see textbook or other references
)1(A
v)(g2ACm
4
f
ffoR
ββββ−−−−
ρρρρ−−−−ρρρρρρρρ====
f
ffoR
A
v)(g2ACm
ρρρρ−−−−ρρρρρρρρ====
Flow in Open Channels and Weirs
1. Rectangular Weir
(Modified Francis Weir Formula)
)g2h)(h2.0L(415.0q 5.1
oo−−−−====
φφφφ====
tan
g2h31.0q
5.2
o
2. Triangular Weir Notch
Note: Both equations apply only for water
Discussion of Problems
NEXT