FLUID MECHANICS
Manila Review Institute Chemical Engineering Reviewfor the November, 2012 Board Examination
[email protected] CP No. 09185663419Dr. Servillano Olao, Jr.
Join the yahoo groups: mrii_che_2012Group homepage: http://groups.yahoo.com/group/mrii_che_2012Group email: [email protected]
Fluid Mechanics Fluid mechanics
Branch of engineering science that has to do with the behavior of fluids (liquids, gases and vapors)
Branches of Fluid Mechanics1. Fluid Statics
Fluids in equilibrium state of no shear stress2. Fluid Dynamics
Portions of the fluid are in motion relative to the other parts
6/18/2012 2S. Olano, Jr. MRII
Nature of FluidsA fluid is a substance that does not permanently resist distortion.
Some physical properties of fluids:a) Density or relative densityb) Viscosityc) Surface tension
6/18/2012 3S. Olano, Jr. MRII
Fluid Mechanics
Types of Fluids1. 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.
6/18/2012 4S. Olano, Jr. MRII
Fluid Mechanics
English SILength, L ft., inch meter (m)Mass, M lbm, slugs KgTime, T seconds (s), hr sForce, F lbf newton (N)Density, 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 lbflbm ftg lbm
lbf s
= = =
2 2SI: 9.806 ( )m mF mg kg kg newton Ns s
= = = 6/18/2012 5S. Olano, Jr. MRII
Fluid Mechanics
A. Fluid Statics and Applications
Hydrostatic EquilibriumForce balance:
- ( ) - 0
0
c
c
gp S p dp S Sdzg
gdp dzg
+ =
+ =
6/18/2012 6S. Olano, Jr. MRII
Fluid Statics and Applications
2 11 2
constant
( )c
c
p gz
gp p g
z zg
+ =
=
Hydrostatic Equilibrium, for constant density (most liquids)
0
0
c
c
pM gdp dzRT g
dp gM dzp g RT
+ =
+ =
Barometric EquationFor an ideal gas, = (pM/RT).
Substituting,
6/18/2012 7S. Olano, Jr. MRII
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 zpp g R T
=
=
(Called the barometric equation)
6/18/2012 8S. Olano, Jr. MRII
Fluid Statics and Applications
2. Simple ManometersPressure balance at level 0:
zggH
ggpp
ggH
gg
agg
zpgg
aggHp
c
mm
c
c
mm
cccc
m
+=
+++=++
)(21
21
Simplifying gives:
6/18/2012 9S. Olano, Jr. MRII
Fluid Statics and Applications
Two-fluid U-tube ManometerPressure balance at point 0:
=
=
+=
++=++
AaHh
hAaHbutghgHpp
gHhpgHhp
m
m
ABBmm
mmBBmA
)()()()(
21
21
6/18/2012 10S. Olano, Jr. MRII
Fluid Statics and Applications
6/18/2012 11S. Olano, Jr. MRII
Other Liquid Column Manometers
Viscous forces in a fluid
Rheological Properties of Fluids
6/18/2012 12S. Olano, Jr. MRII
6/18/2012 13S. Olano, Jr. MRII
B. Fluid Dynamics (Flow of Fluids)
6/18/2012 14S. Olano, Jr. MRII
6/18/2012 15S. Olano, Jr. MRII
Evaluation of Fanning friction factorFluid Dynamics and Applications
6/18/2012 16S. Olano, Jr. MRII
Evaluation of surface roughness factor
6/18/2012 17S. Olano, Jr. MRII
Flow of Incompressible Fluids3. Turbulent flow in pipes and closed channels
(correlation equations for f )
6/18/2012 18S. Olano, Jr. MRII
Blassius Formula: (for smooth tubes)
Colebrook Equation:
Churchill Equation:
6/18/2012 19S. Olano, Jr. MRII
Non-Circular Pipes
6/18/2012 20S. Olano, Jr. MRII
Friction due to Pipe Fittings
Evaluation of Ff (for fittings and valves)
6/18/2012 21S. Olano, Jr. MRII
Entrance and Exit Effects in a Pipe
Entrance Effects for fully developed velocity profile:for laminar flow:
for turbulent flow:
Le
6/18/2012 22S. Olano, Jr. MRII
Exit Effects:
6/18/2012 23S. Olano, Jr. MRII
6/18/2012 24S. Olano, Jr. MRII
Design Charts for Adiabatic Flow of Gases Fig. 6-21, Perry 8/ed
6/18/2012 25S. Olano, Jr. MRII
Momentum Equation
dtmvd
dtdv
mmaF )(=== (Change in momentum)
6/18/2012 26S. Olano, Jr. MRII
Coverage Chart
6/18/2012 27S. Olano, Jr. MRII
Classification of Pumps
6/18/2012 28S. Olano, Jr. MRII
Examples of PumpsA. Centrifugal pumps
Dynamic pumpsB. Reciprocal pumps
Positive displacement pumpsC. Gear pumpsD. Axial flow pumps
6/18/2012 29S. Olano, Jr. MRII
6/18/2012 30S. Olano, Jr. MRII
Examples of Pumps
Examples of Pumps
6/18/2012 31S. Olano, Jr. MRII
6/18/2012 32S. Olano, Jr. MRII
Examples of Pumps
Examples of Pumps
6/18/2012 33S. Olano, Jr. MRII
6/18/2012 34S. Olano, Jr. MRII
Characteristic Curves
6/18/2012 35S. Olano, Jr. MRII
Characteristic Curves of Centrifugal Pumps
6/18/2012 36S. Olano, Jr. MRII
Guide in the selection of Pumps
6/18/2012 37S. Olano, Jr. MRII
System head vs Available head
6/18/2012 38S. Olano, Jr. MRII
Net Positive Suction Head (NPSH) Head available at the pump inlet to keep the
liquid from cavitating or boiling
Where: ps = pressure at suction pointpv = vapor pressure of the liquid
If NPSH
==== 1HH mmv
6/18/2012 40S. Olano, Jr. MRII
Pitot Tube
6/18/2012 41S. Olano, Jr. MRII
Pitot Tube
For Compressible Fluids:
6/18/2012 42S. Olano, Jr. MRII
Flow Metersc) Head Meters (Orifices, venturi meters,
nozzles)
6/18/2012 43S. Olano, Jr. MRII
6/18/2012 44S. Olano, Jr. MRII
Head MetersEvaluation of Y: f (type of fluid)
For liquids, Y = 1.0For gases, see Fig. 10-16, Perry
6/18/2012 45S. Olano, Jr. MRII
Evaluation of C (discharge coefficient)Types of Taps:
6/18/2012 46S. Olano, Jr. MRII
6/18/2012 47S. Olano, Jr. MRII
Friction Loss Due to Flowmeters
Rotameters
6/18/2012 48S. Olano, Jr. MRII
Flow in Open Channels and Weirs1. Rectangular Weir
(Modified Francis Weir Formula))2)(2.0(415.0 5.1 ghhLq oo=
6/18/2012 49S. Olano, Jr. MRII
==== tang2h31.0
q5.2
o
2. Triangular Weir Notch
Note: Both equations apply only for water
6/18/2012 50S. Olano, Jr. MRII
6/18/2012 51S. Olano, Jr. MRII
Discussion of ProblemsNEXT
6/18/2012 52S. Olano, Jr. MRII
6/21/2012 54S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 55S. Olano, Jr. MRII
Solution to Problems
6/21/2012 56S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 57S. Olano, Jr. MRII
Solution
Solution to Problems
hp 622.065.0/550
min/60/48.7/4.62min/4040
550'
=
=
=
hpslbftscuftgal
cuftlbgalftBHP
wWBHPp
6/21/2012 58S. Olano, Jr. MRII
Solution
Solution to Problems
m/s 456.2
100060
4
3600/252 =
==
piSqV
6/21/2012 59S. Olano, Jr. MRII
Solution
Solution to Problems
mba
abRD HH 18.25.12425.144
2244 =
+
=
+==
6/21/2012 60S. Olano, Jr. MRII
Solution to Problems
6/21/2012 61S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 62S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 63S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 64S. Olano, Jr. MRII
Solution to Problems
6/21/2012 65S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 66S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 67S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 68S. Olano, Jr. MRII
Solution to Problems
6/21/2012 69S. Olano, Jr. MRII
Solution to Problems
6/21/2012 70S. Olano, Jr. MRII
Solution
Solution to Problems
KWKWPower 478.054.2124.621445.05001072.2)( 5 =
=
6/21/2012 71S. Olano, Jr. MRII
Solution to Problems
6/21/2012 72S. Olano, Jr. MRII
Solution to Problems
6/21/2012 73S. Olano, Jr. MRII
Solution to Problems
6/21/2012 74S. Olano, Jr. MRII
Solution to Problems
6/21/2012 75S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 76S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 77S. Olano, Jr. MRII
Solution
Solution to Problems
6/21/2012 78S. Olano, Jr. MRII
Solution to Problems
Thank You!!
Manila Review Institute Chemical Engineering Reviewfor the November, 2012 Board Examination
[email protected] CP No. 09185663419
Dr. Servillano Olao, Jr.
Yahoo group: mrii_che_2012Group homepage: http://groups.yahoo.com/group/mrii_che_2012Group email: [email protected]
Fluid Mechanics Lecture Notes 2012Fluid Mechanics Problems