Pharos University
Fluid Mechanics For Electrical
Students
Dr. A. Shibl
Fluid Mechanics
• Is the study of the behavior of fluids at rest or
in motion
• Fluids can be either liquids or gases
• Liquids flow freely and conform to their
containers
• Gases completely fill their containers
Importance Of Fluid Mechanics
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Utilization of Fluid around us; Air, Water…
Prediction of Fluid flow behavior
Sizing or specifying equipment
Estimate the related energy costs
Estimating the system performance under
different conditions
Example
Example
Fluid Properties:
Liquid or Gas
• Liquids are:
– Incompressible, DV ≠ f(DP)
– Viscous (high viscosity)
– Viscosity decreases with temperature
• Gases are:
– Compressible, DV = f(DP)
– Low viscosity
– Viscosity increases with temperature
PRESSURE
• Pressure:
– Force exerted on a unit area
– P = Force/Area
– Pressure acts uniformly in all directions and
perpendicular to the boundaries in the container
Force
– Example: Piston
Area= p/4*D2
P
Pressure=Force/Area
Unit: Psi or Pa (SI)
Density & Sp. Volume
• Density (r) : mass per unit volume
r = mass/volume kg/m3, g/cm3, lb/ft3
– Density is a fluid property and slightly dependent
on temperature
• Specific Volume (n): Inverse of density
n = 1/r
•
m3/kg
Specific Gravity ( SG):
SG=r/rwater At same Temp.
Specific Weight
• Specific Weight = Weight/Volume
g = w/V
• Examples
– Calculate the weight of a reservoir of oil if it has a
mass of 825 kg
– If the volume is 0.917 m3, compute density,
specific weight, specific gravity
Equations for Fluid Property
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Circular Area: Area = p/4*D2
Weight: w = m*g Newton
Density: r = m/V Kg/m3
Specific Weight: g = w/V N/m3
Specific gravity: SG=r/rwater
Viscosity
• Dynamic Viscosity
 = Shear Stress/Slope of velocity profile
F/A
v/ y
cP (centipoise) or Pa-sec
n
F
y
• Kinematic Viscosity
v
Slope = v/y


r
cS (centistokes) or m2/Sec.
Newtonian and Non-Newtonian Fluids
• Two types of fluids: Newtonian and NonNewtonian:
F/A

 Dy 


 
D
v
v/ y
 Dv 
Dy
• Newtonian:
– Ex.: Water, Oil, Gasoline
 Dy 
  f 
 Dv 
Non-Newtonian Fluids
• Time-independent Fluids
– Pseudoplastic (Blood Plasma, syrups, inks)
– Dilatant (Starch in water)
– Bingham (catsup, mustard, toothpaste)
• Time-dependent Fluids
– Electrorheological (behavior changes due to
electric field, particles are present)
– Magnetorheological (iron powders in fluid)
Viscosity Measurement
Falling Ball Viscometer
• Viscosity is determined by
noting the amount of time
a ball takes to travel
between two lines
W
Fb
Fd
  
2
g

g

D
( s f)
18 V
Viscosity Measurement
Saybolt Universal Viscometer
• Measurement is not
based on definition of
viscosity
• Results are relative, so a
standard sample is used
for calibration
• Fast and easy
Saybolt Viscosity
– Saybolt Equations:
n (cS) = 0.226t - 195/t, t< 100 SUS
n (cS) = 0.220t – 135/t, t> 100 SUS
t, amount of time (seconds, SUS, Saybolt Universal
Seconds) it takes for 60 cm3 to flow through orifice
(Saybolt viscometer)
– Example:
• An oil has a viscosity of 230 SUS at 150° F. Compute
the viscosity in cS and cP. Specific gravity is 0.9.
Approximate Viscosities of Common Materials
(At Room Temperature: 70°F)
Material
Viscosity in Centipoise
Water
1 cps
Milk
3 cps
SAE 10 Motor Oil
85-140 cps
SAE 20 Motor Oil
140-420 cps
SAE 30 Motor Oil
420-650 cps
SAE 40 Motor Oil
650-900 cps
Castrol Oil
1,000 cps
Karo Syrup
5,000 cps
Honey
10,000 cps
Chocolate
25,000 cps
Ketchup
50,000 cps
Mustard
70,000 cps
Sour Cream
100,000 cps
Peanut Butter
250,000 cps
http://www.liquidcontrol.com/etoolbox/viscosity.aspx
Viscosity Chart
Temp. ° F


r
 Force
http://www.klassenhydraulics.com/Reference/viscositychart.htm
Temp. C
Hydraulics Fluids for Fluid Power Systems
• Fluid Power
– Pneumatics: air-type systems
– Hydraulics: liquid-type systems
• Hydraulic Fluids:
– Petroleum oils
– Water-glycol fluids
– High water based fluids (HWBF)
– Silicone fluids
– Synthetic oils
Characteristics of Hydraulic Fluids
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Adequate viscosity
Lubricating capability
Cleanliness
Chemical stability
Non-corrosiveness
Ability to resist growth of bacteria
Ecologically acceptable
Low compressibility
Hydraulic Fluids
• HWBF
– Fire resistant
– ~40% oil in water
• Water-glycol fluids
– Fire resistant
– 35 to 50% water
Hydraulic Fluids
• Petroleum Oils
– SAE 10 W, SAE 20-20W (W means rated at
maximum viscosity and cold temperatures)
– Engine oils
– Additives are required to avoid growth of bacteria
• Silicone Fluids
– For high temperature applications
Pressure
• Pressure:
– Absolute = Gage + Atmospheric*
– psia = psig + 14.7 psia
– *14.7 psia at sea level
Pressure Scale
Units of Pressure
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1 bar = 105 Pa = 0.1 MPa = 100 kPa
1 atm = 101,325 Pa = 101.325 kPa
1 atm = 1.012325 bars
1 mm Hg = 0.13333 kPa
1 atm = 14.696 psi
Pressure and Elevation
• Change in pressure in homogeneous liquid at
rest due to a change in elevation
DP = gh
Where,
DP = change in pressure, kPa
g = specific weight, N/m3
h = change in elevation, m
Pressure-Elevation Relationship
• Valid for homogeneous fluids at rest (static)
P2 = Patm + rgh
Free Surface
Free Surface
P2
P1
P1 > P2
Static Fluids: Same elevation and same fluid → same pressure
P2 = Patm + rgh
Manometers
• Used to measure pressure
• DP = gh
Example: Manometer
• Calculate pressure
(psig) or kPa (gage) at
Point A. Open end is at
atmospheric pressure.
A
0.15 m
Water
0.4 m
Hg: SG = 13.54
Pressure Measurement Devices
Manometers
Highly sensitive inclined manometers for
systems demanding precise measurement of
low pressures
Pressure Measurement Devices
Gages
Transducer:
Barometer and Atmospheric Pressure
Patm = rgh
Patm = 14.psi, 1 atm